Dive into the Future with ...   


www VirtualDynamicsSoft com

Javier Montenegro Joo


The Palatinus Development Foundation


VirtualDynamicsSoft: Science & Engineering Virtual Labs

 "Virtual Dynamics"  is the name of an Algorithm created by JMJ in 1988 to Simulate the Stochastic Aggregation of Diffusing Particles (Thesis, San Marcos University).

"VirtualDynamics"  is a Registered Trademark of the Palatinus Development Foundation.  All Rights are Reserved.

VirtualDynamicsSoft is a registered trademark of the VirtualDynamics Dev Org

Intuitively-easy-to-use EduVirtualLabs by VirtualDynamicsSoft

EduVirtualLab:  Educational Virtual Lab created by VirtualDynamicsSoft  

Intuitively-easy-to-use EduVirtualLabs for Computer-assisted education:  Nobody does it better

EduVirtualLabs:   Physics, Math, Digital Image Processing  

Physics Simulators - Mathematics Software

VirtualDynamicsSoft:  Intuitively-Easy-To-Use Software  /  Nobody does it better.

Computer Assisted Learning-Teaching and Distance Education.

EduVirtualLabs to tech / learn Physics, Math and Digital Image Processing.

Intuitively-Easy-To-Use EduVirtualLabs:  Neither Manuals Nor Tutorials Needed.

Hands-on interaction plus Unrestricted virtual explorations. 

EduVirtualLabs for independent study as well as for classroom use.

Physics Simulation with EduVirtualLabs for learning while having fun.

<<< <<   Table of Contents    >>>>>

------- Mathematics ---------

    Mathematics Edu Virtual Lab  77   

Plane Analytic Geometry ( PAG ) EduVirtualLab

   Curvilinear:  Easy Learning Plane Analytic Geometry        

   Panageos:  PAG  Problem solver  

-------- Physics -------------------

Physics Virtual Laboratory,  PVL :  191  Simulators

 PVL: Mechanics   

  PVL: Oscillations (Waves and Oscillations)

 PVL: Electromagnetics (Electricity and Magnetism)

  List of General Physics Simulators:  191 

Mathematical Physics Computer Games:   MathPhysicsGames

-------- Digital Image Processing -------------------

Imagery : Digital-Image-Processing EduVirtualLab    ( 44 modules)

------- How Physicists do it --------------

 In highly degenerate states Physicists do it ....

------- Special Topics -----------

Chaos, Percolation, Stochastic Aggregation, Cellular Automata, etc,

Special Topics Simulation Software

   Audio Visualizer :    Audio-visual file explorer    

------- General Information -----------

Minimum System Requirements

  Ordering Information  and  Free Upgrades

 Order online - Buy software

 Contacting the Author:  Javier Montenegro Joo



 <<< Download Demos:   Click link  >>>

Download  Physics Virtual Lab (PVL)  Demo

Download_Math Virtual Lab (Visual Math) Demo

Download_Imagery  (Digital Image Processing)  demo

Download Curvilinear-Panageos Demo

  Download  EasyTOEFL_Demo 

    Download   AudioVisualizer Demo     

   Download  EconoModeler Demo    




Javier Montenegro Joo,  The VirtualDynamics Research & Development Organization.





Javier Montenegro Joo

The software exposed in this document is just a fraction of the material developed by  Javier Montenegro Joo (JMJ),  who  simultaneously studied Physics and Computer Science, graduating as a physicist in San Marcos University (Lima - Peru),  he worked as a scientific-applications systems analyst and computer programmer in the Peruvian Geophysics Institute (IGP),  carried out graduate studies -Master of Science and Doctoral degrees- in The Ohio University (USA) and in Sao Paulo University (Brazil), respectively.   In Ohio he was involved in the-transition-to-chaos in non-linear systems computer simulations. In Sao Paulo JMJ worked on Algorithm Development for Cybernetic Vision (Invariant Pattern Recognition), executing research and development based on Neural networks, Genetic algorithms, and Polar Hough transform, and creating an ultra efficient system for Invariant Pattern Recognition of Polygonal Objects, which has successfully been applied to the computerized detection of geometrical imperfections in rectangular biscuits, chocolates and in mechanical pieces.

Mr. Joo is an ICTP (Italy) Associate member,  he develops  simulation software for research and for Computer Assisted Education,  under the auspices of The Palatinus Development Foundation.  As a university faculty (more than 12 years teaching experience),  he is a lecturer of Mathematics, Physics, Data Structures and Digital Image Processing.                   He has conducted five research projects on Stochastic Aggregations with support of the National Science and Technology Council (concytec).
JMJ's Physics research experience includes the development of algorithms to simulate and visualize Stochastic (DLA-type) and Regular (Cellular Automata) Aggregations.  JMJ devised the Selective Dynamics Releasing Frame, an algorithm to speed-up computer simulations of stochastic aggregations.  JMJ has also devised and developed Virtual Labs for research on Percolation phenomena and on Chaos in non-linear systems.

In the Artificial Intelligence field, specifically on Computer (Cybernetic) vision,  JMJ has carried out research and development on Neural Networks whose architectures are designed through Genetic Algorithms. 
Mr. Joo's  teaching experience started when he  was a graduate student in USA, then he worked as a Teaching Assistant in the Physics Departments of  The University of Pittsburgh and of  The Ohio University, in both universities  he was as a Physics Laboratory  Instructor.
In 1988, J.M.J. created the algorithm  "Virtual Dynamics" (based on the DLA Algorithm) to                                             Simulate the Stochastic Aggregation of Diffusing Particles around a static seed.                                                     (Dissertation, Physics Degree of Licentiate, San Marcos University).  The different colors in the object on the right side indicate the order of arrival of the diffusing particles to the growing aggregate, it can be seen that late-arriving particles can not get inside the object due to the screening effect of particles already in it. 

The author's fields of interest and experience include:   Mathematical Modeling,  Algorithm Development for Mathematical Programming,  Digital Image Processing in Scientific Applications, Monte Carlo Simulations, Development of Algorithms for Computer Simulation and Visualization, Pattern Recognition, Neural Networks, Computer Graphics, Algorithmic Art, Genetic Algorithms, Cellular Automata and software for Computer Assisted Instruction and Learning.


The VirtualDynamicsLabs  experience


Since 1990 JMJ´s enterprise, VirtualDynamicsLabs  has been designing and developing software for Science & Engineering applications, and since  1995 VirtualDynamicsLabs   has also been designing, developing and marketing  software for Computer Assisted Education ( EduVirtualLabs ) in Physics, Mathematics, Digital Image Processing, and related themes.   JMJ is the founder of VirtualDynamicsLabs   and he is also the creator of the VirtualLabs..

The proprietor of the name  " EduVirtualLab "  is VirtualDynamicsSoft.                                                                                            " EduVirtualLab "  is the generic denomination (trademark) of any Educational Virtual Lab created by VirtualDynamicsSoft.

 Back to Table of Contents 




 Digital Image Processing

 Imagery:  Digital-Image-Processing EduVirtual Lab                    (44  Modules)




Image Fusion with Imagery

Below:  three different instances

 of Controlled Image Fusion

of the two images at the top.


Imagery EduVirtualLab

With the aim on making sure the learning of Digital Image Processing (DIP), the theory sustaining each process realized by Imagery is included on each module, it also appears in an extensive way in the Class Notes (pdf format) accompanying Imagery, which are used by the author in his classes of DIP for graduate students of Sciences and Engineering.

IMAGERY is a Digital-Image-Processing EduVirtualLab created by Javier Montenegro Joo. 

 IMAGERY operates on images supplied by the author and also on those of the user.


Left:   Histogram-aided edge detection of a grey-leveled image.

With Imagery the histograms of three images may be extracted and compared

This module shows an algorithm for Image Segmentation. The input image contains several objects and these have been extracted one-by-one with a segmentation algorithm.


Controlled Image fusion:  The two images at the top are the input images to be fused. Below are the output images.  The user sets the percentage of each image in the fusion.  It is also possible to ignore one of the colors in the input images.  With Imagery up to three images may be fused in the proportions set by the user.


The modules of Imagery include the pertinent theoretical background of the themes it covers, in this way the user knows at every moment the mathematical transformations operating on the images and how they operate.

Grey-leveled image edge detection with the Sobel's Gradient (first derivative).  Three different gradient thresholds set by the user can be appreciated at a  time.

User defined Convolution filters.

Imagery allows the user to test his own convolution filters. Up to three instances of filters designed by the user can be simultaneously visualized, thus allowing filter effects comparison.

In the figure, the image at the top left is the input image, the others are the output images resulting after applying three different user defined filters.


Modules in Imagery   ( 44 )

Color (05)
          01 Color Synthesis
          02 RGB Color mixing
          03 Color To Grey-Level Transformation
          04 Color Filtering in images
          05 Image Brightness and Darkness
Edges (09)
          01 Edge Enhancement by First Derivatives and Gradient
          02 Edge Enhancement by Gradient: The Roberts Operator
          03 The Prewitt Operator
          04 The Sobel Operator
          05 Generalized Sobel Operators
          06 Edge Direction Detection through Gradient
          07 Edge Enhancement via the Laplacian Operator
          08 High Boost Filter (Fine detail enhancement)
          09 Comparison of Sharpening Filters
Convolution (02)
          01 Spatial Operators (Convolution Filters)
          02 User-Defined Convolution Filters
Geometry (06)
          01 Representing a Straight Line
          02 Circularity (Binary images)
          03 Translations
          04 Rotations
          05 Size Scaling
          06 Shearing
Masks (03)
          01 Point && Small Hole Detection Mask
          02 Line Detection Masks
          03 Noise-Reduction Median Filter
Transformations (07)
          01 Image Transformations
          02 Erosion of Binary Images
          03 Dilation of Binary Images
          04 Image Subtraction
          05 Thresholded Image Difference
          06 Controlled Image Fusion (2 images)
          07 Controlled Image Fusion (3 images)
Histograms (05)
          01 Histograms (Grey-leveled images)
          02 Histograms: Compare the histograms of three grey-leveled images
          03 RGB Histograms
          04 Binarizer: Conversion of grey-level to binary images. Thresholding
          05 Borderliner: Histogram-Assisted Edge Detection of grey-leveled Images
Segmentation (01)
          01 Binary Image Segmentation through Wrapping
Miscelaneous (01)
          01 Binary Image Boundary Detector
Pattern Recognition (05)
          01 Signatures: Pattern Centroidal Profile Representation
          02 Massive RTS-Invariant Moments
          03 Boundary RTS-Invariant Moments
          04 The Polar Hough Transform
          05 Hough-Transform-based Line Detector

   Prices (USA dollars) :       Personal use:   75.00                              Institutional use:  350 (Quantity discounts)

Download Demo:  Imagery: Digital Image Processing

 Back to Table of Contents        Order online  - Downloads 



Mathematics EduVirtualLab



Mathematics Edu Virtual Lab   ( 77 modules )

The Math Virtual Lab (MVL) is a mathematics visualizer useful from high school to university.

Download Demo of the  Visual Math = Math Virtual Lab:      

Math Virtual Lab (MVL): VisualMathDemo


Math Virtual Lab is a highly interactive visualization EduVirtualLab addressed to High school, College and University students.  This is a very powerful tool that helps to learn and solve problems by the hundreds in a very short time. 



Left: The Trigonometric Circle,  visualizes the behaviour of Sine, Cosine and Tangent as the angle is varied either manual or randomly. A Degrees-to-Radians (and viceversa) transformer is built in.

Left: The Logarithm Function

The user can generate any number of plots of the Logarithmic Function for any Base b between 0.05 and 15.00; the corresponding numerical values are listed on the column on the left side.

In all Visual Mathematics modules the user may print the image or only the generated values. All modules include theory and pertinent information 

Left: Circle & Angles Theorem III: Angles Subtended by an Arc in the same Segment of a Circumference are Equal


The user can click and drag the vertices with the mouse and see the geometrical effects and corresponding numerical values.

 Math Virtual Lab (MVL):  Maximum Mathematical Experimentation and Visualization:  Impossible not to learn !!!

Math Virtual Lab modules include the theory necessary to understand every theme.  Every student should have this powerful tool at home.


The user can click and drag the vertices with the mouse and see the geometrical  effects and corresponding numerical values.

Left: The Quadratic Function

The user enters the coefficients A, B and C of   y = Ax^2 + By + C ,  the module plots the function, finds the roots (real or complex), detects the vertex and focus coordinates.  Includes eight pre-defined examples. 

Left:  Remarkable lines and Points in the Triangle.

As the user drags with the mouse the vertices of the triangle, the Altitudes, Medians, Mediatrices and Bisectrices, as well as their corresponding intersecting points are shown.  Equilateral, Isosceles and Random triangles may be generated with a button click.  Coordinates of vertices and remarkable points are reported. It is also possible to work separately with every remarkable line and point.

Teachers use Math Virtual Lab to prepare homeworks and tests in a short time.


 With Math Virtual Lab the student solves homework problems while he/she really learns and enjoys mathematics.


Math Virtual Lab (MVL) includes the following  77   modules 

<><><> Arithmetic ( 08 )

  1. Prime Number Detector. 

  2. Leap Year Detector.

  3. Factorial calculator.

  4. Decimal-Fraction to Common-Fraction Transformer.  

  5. Greatest (Maximum) Common Divisor,  GCD   (Detects the  GCD of up to 4 numbers)

  6. Least (Minimum) Common Multiple,  LCM   (Detects the LCM of up to 4 numbers)

  7. Progressions (Arithmetic and Geometric, Terms addition, Interpolations, etc)

  8. Base Change: Converts a Base-10 Integer Number into another Base

<><><> Algebra ( 11 )

  1. Computation of 3x3 Determinants.  

  2. Computation of 4x4  Determinants.

  3. Matrix Inversion ( 2x2  -  3x3 ).

  4. Quadratic Equation Solver:  Ax2 + Bx + C = 0

  5. Given the roots, construct the quadratic equation    Ax2 + Bx + C = 0

  6. Graphic Solution of the quadratic equation: Parabola, roots, vertex, focus.

  7. Solver of systems of two simultaneous equations with two unknowns.  

  8. Solver of systems of three simultaneous equations with three unknowns.

  9. Linear equation plotter:   Ax + By + C = 0   (slope, inclination, X-Y-axes intercepts)

  10. Graphic solver of a system of two simultaneous linear equations.

  11. Given the sum and the product of two numbers, find the numbers.  

<><><> Geometry ( 24 )

  1. Angles (Degrees, Bisector)

  2. Arc Length 

  3. Circular Crown ( Computes Area, perimeter, etc)

  4. Circular Sectors:  (Variable angles and radii.  Compute Area and Perimeter)  

  5. Triangle Basics:  Area, Perimeter, Angles, Angles Sum, Classification

  6. Triangles: Perimeter, Area,  Inner angles add up to 180°

  7. Triangles: Detects Orthocenter, Baricenter, Incenter, and Circuncenter in any triangle.

  8. Pythagorean Theorem:  Solves problems and depicts triangle.  

  9. Regular Polygons ( 3 to 72 sides) Inscribed-in  or  Circumscribing Circles.

  10. The Rhombus:  Computes Perimeter and Area.

  11. Regular Polygon Designer (  3 to 72 sides). Circle designer. 

  12. Heron's Equation: Given the sides of any triangle, computes its area.

  13. Quadrangles (Angles, Side Lengths, Perimeter, Diagonals, Convex, Concave)

  14. Parallelograms (Inner Angles, Perimeter, Altitude, Area)

  15. Trapezoids (Inner Area, Perimeter, Middle Base, etc)

  16. Polygons (User made, Diagonals, Inner angles, Convex, Concave, etc)

  17. Regular Polygon ( 3 to 72 sides) Vertex Coordinates (Cartesian and Polar)
  18. Secant (User-controlled inclination) to parallel lines (angles formed).
  19. Circle & Angles: Angle at the center of a circle and angle at the circumference. 
  20. Circle & Angles: Quadrilateral inscribed in a Circle (Opposite angles add up to 180°). 
  21. Circle & Angles: Angles subtended by an Arc in the same segment of a circumference are equal.
  22. Radius of a Circle Circumscribing Triangle of known Sides. 
  23. Circle Inscribed in a Triangle of known Side Lengths.
  24. Partial Areas.

<><><> Trigonometry ( 07 )

  1. Angles: relationship between degrees and radians. Conversions.

  2. Cosine Law: Given the sides of a Triangle, compute its inner angles and depict it.

  3. Trigonometric Circle (Sine, Cosine, Tangent,  Signs, Quadrants, etc)

  4. Graphs of Trigonometric Functions and their combinations.  

  5. Given Two Sides of a Triangle and the comprised angle, get its Area.

  6. Sine and Cosine Automatic Curve Generation.

  7. Tangent Automatic Curve Generation.

<><><> Plane Analytic Geometry ( 08 )

  1. Conic Sections (Eccentricity, Circle, Ellipse, Parabola, Hyperbola)

  2. The Straight Line ( Slope, Inclination, Equation, Distance between two points, etc).  

  3. Equations of the Straight Line.   

  4. The Parabola( Equation, Latus Rectum, Directrix, etc).

  5. The Ellipse (Equation, Vertexes, Foci, Axes, etc) 
  6. The Parabolic Antenna (Application of Parabola Property).

  7. Circunference through three Points
  8. The Hyperbola

<><><> Miscellaneous ( 15 )

  1. The Greek Alphabet.

  2. Vectors: Components, Sum, Difference, Angle between two Vectors, etc.

  3. Polar Coordinates. 

  4. Complex Numbers. 

  5. Chaotic Dynamical Systems: Logistic Equation Return Map ( Iterations ).

  6. Rotations (User-made polygons)

  7. Translations (User-made polygons)

  8. Size Scaling (User-made polygons)

  9. Shearing (User-made polygons)

  10. Computing the number Pi
  11. The Definite Integral: Area under the curve y = f(x)

  12. The Logarithmic Function

  13. Noticeable function

  14. The Linear Function 

  15. Cubic Bezier curves 

<><><> Notable Curves (04)

  1. Cardioiod

  2. Cardioid genesis

  3. Limacon of Pascal

  4. Archimedes Spiral

Prices (USA dollars)  >>> Personal use:   65.00 ...... institutional use:  180.00 (Quantity discounts)

  Order online  - Downloads                                                        Back to Table of Contents   

How physicists do it ....

How physicists in highly-degenerate states do it

Javier Montenegro Joo

Obviously, you must be physicist to understand this

Below is the list of conclusions I arrived to when I was a physics student. Only the mind of an unconcerned young man can conceive these thoughts while he is apparently paying attention in the classroom. Then it was already known that physicists do it with models, I may add that in highly-degenerate states, physicists do it .....


With a cat (Schrodinger's), with twins (Einstein's) ...

With Strange Attractors, with Random Walkers, with Annihilators, ...
With Models in Super Positions and with Chaotic Motion. 
With Rigid Bodies moving Back and Forth with Friction.
Spontaneously with Random Walkers on Inclined Planes.
With Random Motions with The Nearest Neighbors.
With Chains (Markov's), Vacuum pumps, Vibrators and Strings. 
With Self-Excited Motions in Closed Isolated Environments.
Approaching the Critical Point with Noisy Vibrating Bodies
Swinging back and forth and with transverse oscillations.
With Intermittency, with Noise, With Distortions and Aberrations.  
And obviously, dissipating energy in the form of heat.

  Back to Table of Contents 

Plane Analytic Geometry EduVirtualLabs

Computer-Assisted Plane-Analytic-Geometry
Curvilinear & Panageos
Curvilinear and Panageos are two EduVirtualLabs oriented to the understanding and mastering of the subject of Plane Analytic Geometry.  Both  have the same screen appearance, they are intuitively easy to use, there are no manuals needed, no need to invest time to learn how to use.   The whole screen may be printed or only  its left-hand-side column containing the reports of all operations made. 
With two mouse-clicks for every object the user obtains plentiful information. For instance, pressing the line-icon and then clicking two points on screen, the following information is generated: coordinates of the points, line equations (linear, xy-intercepts, slope-y-intercept), line slope and angle of inclination and the line intercepts with the axes of coordinates. Another example, pressing the circle-icon and clicking two points on screen, the produced report contains: coordinates of center (first click), coordinates of a point on circle edge (second click), coordinates of diametrically opposed point, radius length, circle equations (short and general form), area and perimeter.  Last example, clicking three points (triangle vertices) and then pressing the icon showing a triangle with its altitudes, the program reports the three altitudes of the triangle, linear equations of the three altitudes and three sides, their slopes. the intersecting points of the altitudes with the triangle bases.
The following table shows the icons for objects and operations in both,  Curvilinear and Panageos.

 Back to Table of Contents  



Easy Viewing Plane Analytic Geometry,   The best way of really learning while visualizing the solution to problems.  This is an EduVirtualLab for the person who really wants to learn Plane Analytic  Geometry (PAG), or for the person who loves visualizing it.  This is a tool that helps to grasp a conceptual understanding of  PAG while visualizing the solution to problems by hundreds in a very short time. 

The range of problems solved by Curvlinear goes from the most simple up to for example finding the  linear-equations of the heights of a triangle, or the equation of the line through the intersections of two circles, Or the extended  equation of the circle passing by three given points (see the icons).  

Admits two types of  coordinates input: either mouse or keyboard.   

The image on screen as well as the textual reports may be printed at will, just click a button.

  Order online  - Downloads             Back to Table of Contents          E-mail the Author  

Download Curvilinear-Panageos Demo

Prices (USA dollars) Curvilinear >>> Personal use:  35.00 ...... institutional use:  140.00



Plane-Analytic-Geometry Problem Solver, is for the user who already knows the subject and wants to verify his/hers solutions, or for the teacher or student who needs to solve hundreds of problems in a very short time.

 Teachers may use this software to quickly prepare classes and also to propose and try  problems for tests and exams.  Students may verify their hand-made solutions with this tool.

Multiple keyboard-input modes. Reads and interprets many types of equations supplied by the user.  Includes a quadratic equation solver. 


The image on screen as well as the textual reports may be printed at will, just click a button.


Panageos is Not recommended for beginners. 

  Order online  - Downloads         Back to Table of Contents          E-mail the Author

Download Curvilinear-Panageos Demo

Prices (USA dollars) Panageos >>> Personal use:  35.00 ...... institutional use:  140.00



Mathematical Physics Computer Games

MathPhysicsGames:   This is a set of interactive and audio-visual Computer Games based on Mathematical Physics Modeling.  This software allows the user to assess the application of Physics and Mathematics in the development of amusing Computer Games, these kind of Computer Games not only improve the alertness and speed of reaction of the user,  they also boost his/her interest in Physics and Mathematics.   These games make use of Physics and Mathematics topics like Parabolic Motion, Velocity, Acceleration, Velocity components, equations, curve intersections, etc, etc.

List of Computer Games in MathPhysicsGames:


(1) Shoot Down The Ufo:  the Ufo flies on Parabolic, Sinusoidal, or lineal orbits. The user controls the Cannon elevation angle with the mouse and fires at will.  

(2) Shoot Down the Airplane:   User-controlled cannon and firing.

(3) Hit the Tank:  The user drops bombs from the flying airplane on a moving tank. 

(4) Bouncings: a ball bounces on the borders of a table, only if these are activated by the user.


Games have four levels of difficulty and constitute a serious challenge to the user.


 Use with caution, these Computer Games might boost your attention and alertness,   increase your speed of reaction and coordination and foster your interest in Physics and Mathematics


These games are included in the Physics Virtual Laboratory, PVL                        

   Back to Table of Contents                                               See the PVL       

PVL:  Mechanics

Physics Virtual Lab (PVL):  Mechanics

EduVirtualLab on Mechanics

These are some of the Mechanics simulation modules included in the PVL

<<< Elastic Collisions: The Bouncing Ball

The user sets the Coefficient of Restitution, The Initial Height and the first Bouncing Angle.  The module makes the simulation along with the visualization and reports successive bouncing angles, heights and velocities.

Friction on a tilted plane.

The user sets the Mass Weight and the Kinetic Friction Coefficient, then he/she clicks a button to little by little tilt the plane, the block slides down when the elevation angle reaches the corresponding sliding angle. 

Wheel Gearing

The user sets the number of wheels ( 2, 3 or 4 ), their radii, the linear velocity and the rotation direction.  The wheels rotate the angles corresponding to their actual Angular Velocities so that its dependence on radius length is evident. As the wheels rotate, the module reports: Angular Velocities, Number of turns, Angular displacement and linear displacements (same for all wheels). 


Projectile Flight Simulator     (parabolic Motion)

The user sets the shooting velocity, cannon elevation angle, horizontal and vertical air resistance, and acceleration of gravity. The simulator makes the corresponding simulation and visualization. Reported data: Horizontal range, Highest altitude, flight time.

Whenever the projectile flight is paused (at user's will),  the velocity vectors are displayed. Several trajectories can be displayed simultaneously.

Uniformly Accelerated Motion Data Plots Generator

The user sets the Initial Velocity, Positive or Negative Acceleration, Delta Time, and Number of Steps, and the software generates the numerical results and plots of:  

(1)  x(t) = Vo t + (1/2) a t ²

(2) V(t) = Vo + a t

(3) Delta X(t)

(4) V(x) = Sqrt[ Vo ² + 2 a x ]

thus the user can analyze the resulting data and plots. It is also possible to generate "Real-Life, Experimental" data,  these can be saved and used to feed a plotter.

Behavior of velocities (V, Vx, Vy) in the Parabolic Motion

The user sets the Elevation angle of a cannon in the origin of coordinates and its shooting velocity Vo, the module makes the plottings of projectile velocities V, Vx, Vy,  as time goes by


  List of  Simulators in PVL Mechanics                         See the Physics Virtual Laboratory, PVL   
  Order online  - Downloads        Back to Table of Contents      


PVL: Electromagnetics = Electricity and Magnetism

Physics Virtual Lab (PVL):       Electromagnetics
EduVirtualLab on Electromagnetics

These are some of the Electricity & Magnetism simulation modules in the PVL

<<< Electric Fields and Equipotential Surfaces due to point charges.   The user places any number of point charges (positive or negative) by clicking with the mouse on screen, the charge-disposition is fixed also by the user, then  clicks a button to get either the Electric Field or the Equipotential Surface of the group of charges. 


The Electric Transformer

Computes input/output Voltages, Number of Spires, Power and Electric Currents.


Resistance and Dissipated Power in an Electric Circuit.  The user controls the Resistances, the Emf, the internal resistance. 

Induced Electromotive Force on a square loop traversing a magnetic field. 

The loop displaces either automatically or manually (the user moves it with the mouse).

Works with inwards or outwards magnetic fields.  Plots magnetic flux on loop, shows clockwise, null and anticlockwise induced electric currents.

The user sets the values of the magnetic induction B, loop side length and velocity.

Electric circuits

Left: As the user sets the Electromotive force, the internal resistance and the resistances in the resistors, the program reports the  electric currents, voltage drops, dissipated powers in the whole circuit and in individual resistors.

Left: Charged particle Deflection by an Electric Field, the user sets the E-Field intensity, mass, charge and initial velocity of the charged particle.

  List of  Simulators in PVL Electromagnetics                    See the Physics Virtual Laboratory, PVL   
  Order online  - Downloads                                              Back to Table of Contents     



PVL:  Waves and Oscillations

Physics Virtual Lab (PVL)  ---  Waves and Oscillations

EduVirtualLab on Waves and Oscilations

These are some of the Waves & Oscillations simulation modules in the PVL

<<< The Damped Oscillator:  In order to appreciate the effect of the damping, the oscillation starts in a free environment, then on a sudden a damping material surrounds the oscillator.

Total Energy Distribution in the Simple Harmonic Motion.  

The exchange between the Kinetic and the Potential energies is appreciated as the Spring oscillates conserving its Total Energy.  The user controls the Mass, and the Elastic constant k.

Standing (Stationary) waves

Clearly visualizes a wave traveling to the right side, another wave going to the left side, and the standing wave produced by their  interference. Obviously the user controls the Amplitude, Wavelength, Frequency, etc.  Also it is possible to freeze the time, and to visualize the motion of individual waves


Damped Harmonic Oscillations Analyzer

Under damping, Over damping and Critical Damping.

The user sets the Mass, Elastic constant k, Viscosity b, Initial Phase, Delta Time and Number of events, the module generates the data and makes the corresponding plotting.

The user may analyze the generated numerical data and the plots.  Prints the whole image or only the generated numerical results.  

Simple Harmonic Motion: The Rotor

Superposition of two Simple Harmonic Motions in the same direction

Genesis of the Lissajous Figures.

In this module it is shown how two perpendicular SHM oscillators generate the Lissajous orbits.

The user may test with all the parameter combinations he wants.  An option to generate random combination of parameters is included

  List of  Simulators in  PVL Oscillations                             See the Physics Virtual Lab, PVL   
  Order online  - Downloads                                         Back to Table of Contents     


Physics Virtual Laboratory,  PVL

Physics Virtual Lab,  PVL       ( 191  Simulators )

What the Physics teacher gets when using the PVL:

The creator of the PVL teaches Physics to science and engineering students at the university, his experience is that when teaching with the PVL:

(1) The classes are more amenable, because instead of showing a static drawing the professor displays a dynamic simulation, hence students understand quicker and easier.
(2) The PVL makes classes more efficient because the professor invests less energy and achieves more in a shorter time.
(3) When dealing with some not-so-intuitive themes, students request viewing a simulation to understand.
(4) Usually students request to repeat the simulations with different parameters to see what happens and understand better.
(5) At the end of the class, students have a feeling of having understood the theme dealt with.
(6) The professor invests less time preparing questions for exams, because the PVL modules create problems and show their solutions, additionally some PVL modules are expressly made to generate Physics problems

Download PVL Demo:          Physics Virtual Lab, PVL: PVL_Demo

Besides hundreds of individual users around the world, the following Universities and High Schools have purchased Institutional Licenses of the PVL for students instruction:   

- Physics Dept of Central Connecticut State University (CCSU - USA)

- Universidad ESAN (Lima Peru)

- UCAN ( Angola, Africa)

- St Petersburg High (FL, USA)  

- San Marcos University (Lima - Peru):  Every summer the university offers a training workshop  "Physics Teaching  with computers"  a course with the PVL addressed to high school and university physics teachers.

See some of the Mechanics modules of the PVL     PVL Mechanics 

See some of the Waves and Oscillations modules of the PVL     PVL Oscillations  

See some of the PVL Electricity & Magnetism simulators   PVL Electromagnetics 

The  PVL  is an EduVirtualLab of Physics, is Audio-Visual, it contains detailed simulators of phenomena from Mechanics, Hydrostatics, Waves, Hydrodynamics,  Electricity, Magnetism, Thermodynamics, Optics, Applications, etc, etc.   

PVL is a professional virtual lab that leaves behind simple demonstrations and rather puts emphasis on very precise simulations under the direction of the user.     

Here only a few of the simulators from the package are shown, the complete list of simulators is included below. 

<<< PVL : Stereo Sounds >>>

The PVL is the Non-Plus-Ultra of the Physics Simulation Softwares, this Virtual Lab includes detailed simulation modules dealing with Mechanics, Waves, Oscillations, Thermodynamics, Electricity, Magnetism, Light, Optics, Hydrostatics, Applications, etc.   The main feature of PVL is that every user can adapt it to his/her own level.   The PVL is mainly addressed to the university student / teacher of Sciences and Engineering, however, since a variety of different-level books have been used to develop PVL, it becomes also suitable for Physics courses in Colleges and International Baccalaureate Programs.  High School students will find many modules of PVL helpful to simulate and visualize many Physics topics covered in their courses.

Physics lovers and amateurs will find in PVL very stimulating and enlightening experiences while learning at their own pace.  

VirtualDynamicsSoft Professional and Rigorous Simulators execute Mathematical Models:  whenever there is an equation or  mathematical model to represent an experiment or physical event, it has been used in  PVL  to produce its simulation. In order to visualize the simulation while this takes place the more advanced techniques have been used, the result is a professional and robust software.

Dispersion of a beam of white light by a drop of water.     Origin of the rainbow: Three sets of emergent rays are shown.

The incident light is decomposed into the visible spectrum.

The user sets the size of the drop of water, the position of the light source and the point where the incident ray hits the drop.

The module also displays the Visible spectrum of light on a horizontal bar.

Magnetic deflection of a charged particle

Charged particles hit a region where there is a magnetic field,  the particles interact with the magnetic field and their trajectories are deflected

The user sets the magnetic field (magnitude and direction), the charge, mass, velocity and the incidence angle of the particle.


 Some modules of the PVL have a "Lab Guide" to be used as the set of instructions to be followed during the physics lab sessions at schools and universities

Simultaneous visualization of several events

Some simulators of PVL allow simultaneous visualization of three or four different instances of a physical phenomenon, this boosts learning by comparing different cases and hence helps to understand the phenomenon.


Left:  A vibrator simulator showing three different frequencies. Since the user sets the frequencies of the vibrator, a huge number of frequencies may be visualized and compared. Impossible not to learn !!!.

Deviation by a Prism.-

The user sets the Refractive Index of the prism and its top angle.  As the angle of the Incident Ray is varied with the mouse, the Refracted Rays and the Total Deviation Angle are shown, also their numerical values are reported. The Minimum Deviation of the prism is clearly appreciated when the ray inside the prism is parallel to its base. 

This module plots Total Deviations  vs   Incident Angles for user-fixed values of the refractive indices  

Physics Virtual Lab, PVL,  is  interactive and very easy to use, there is no need of either manuals or training or tutorials. 

This is a tool recommended not only to students and teachers but also to the persons fond of Physics, those who really love this subject.  Obviously secondary schools with ambitious teaching programs and universities, may use this software instead of the traditional laboratories, which are expensive, fragile, hard to maintain, limited, ....

Left: Operation of the Four-Cycle Piston Motor.

Intuitively Easy-To-Use simulators.

Users do not need to get trained to operate these simulators. At any moment during use, non-applicable controls (options,  buttons, parameter changers) are disabled and only appropriate controls are enabled, in this way there is no chance to activate a non-opportune control.  For instance the buttons to abort or pause an experiment are disabled at any time except while an experiment is running.

<<< The Carnot Engine: Converting Heat into Work.  As the piston displaces due to the expansion or  compression of the gas inside the cylinder, the two Isothermals and two  Adiabatics of the Carnot Cycle are plotted.  Pertinent theoretical explanations are shown as every stage of the Carnot cycle takes place.

Mass Falling Down due to the Gravity in a Medium whose Resistance is Proportional to the Velocity of the Mass.

The user sets the Resistance of the medium, the initial velocity of the falling mass, the number of events and the delta time, the software makes the corresponding data generation and plots Position, Velocity, Acceleration and Delta Position.    Allows data collection from simulated real-life experiments.

A similar module dealing with Motion against a Resistance proportional to  V ² (squared Velocity) is also included in PVL

Tri-Dimensional Lissajous

Superposition of Three Simple Harmonic Perpendicular Oscillators. The user controls oscillator amplitudes, frequencies and phase varying, as well as image orientations, displacements and animation speed.  Several animations (manual and automatic) are possible. Lissajous orbits may be seen from any angle. 

PVL is Audio-Visual:  whenever it is pertinent, simulators include stereo sounds, for instance when a bomb hits the ground, the sound of a explosion is produced, a collision of two cars on the air track is accompanied by a knocking sound.

Learning by comparison.- 

Tracks of experiments on screen have different colors (for instance, projectile trajectories) and them may be kept for comparison, in this way the effect of changing parameters can be easily observed.  The data associated to every experiment is displayed with the color of the track of that experiment, in this way, tracks and data are easily identified and compared.



No passive user.-  The PVL  is strongly dedicated to animation and simulation with user's data. For instance in the case of the Doppler Effect, up to twelve wave fronts are generated one after other and their expansion process is visualized while the wave source keeps displacing.  Obviously time may be frozen for as long as the user wants, so that he/she can see what is taking place and analyze the situation. This module includes a collection of sounds that when activated by the user, reproduce examples of the Doppler effect.

Use the screen as a blackboard ....

Whenever an experiment or demonstration occupies small space, several instances of it may be displayed wherever the user wants on screen, like on a blackboard.  In this way several cases of a  topic  may be appreciated at once on screen, thus facilitating understanding and learning, obviously the instructor's work becomes easier and much more productive.

Pre-defined examples.-  In general, whenever the objective of  an experiment is not obvious, the simulators include a set of pre-defined examples, in this way the user may execute first these examples and then after the experiment is understood, he/she may try with his/her own parameters.

Time freezing

Time can be frozen at any moment during simulation, it is then when pertinent vectors (velocity, force, etc) are displayed.  In real-life experiments neither time can be frozen nor vectors are seen, by the other hand, on a blackboard, vectors are seen only where the teacher depicts them. These simulators enable users to watch pertinent vectors wherever and whenever they want and as many times as desired by just clicking a button.


Unrestricted experimentation.-   Unrestricted experimentation leads to learning through extreme-situations exploration.  Physics Virtual Lab allows for this type of experimentation since the user may try experimenting with data sets that in real life may be impossible or may even harm the user.  For instance, in a conventional laboratory it may be impossible an exaggerated elongation of a spring, since it may break the instruments, or may encounter obstacles or may even hurt the user if suddenly released.

A Laboratory at home

For the person who enjoys physics and wants to appreciate it comfortably at home, this software is the ideal tool.

Screen Printing

Screen images may be printed, just click a button (see included images). 

Text Printing

Some modules generate abundant data in text form, this can be printed as a text file with just a click on a button.

Author easy to reach

Users may contact the author by e.mail or telephone at any time, for suggestions and doubts.  The author thanks in advance for  ideas and criticism to improve this material.

Left : Electromagnetic wave front polarization.-    

The user sets Amplitudes Ex and Ey of electric fields, their  initial phases and wave front polarization type.  Every time the experiment is paused the electric field E and its components Ex and Ey may be seen. Pre-defined examples are also included. Up to four cases may be conserved on screen with their respective parameters.

Left : Adiabatic Compression or Expansion of an Ideal Gas.- The user sets Cp / Cv, temperature and pressure, a button click starts the piston movement. The plots are made as the piston displaces. The gas inside the cylinder changes color as its pressure is varied.

Theory and Equations

Every PVL module includes pertinent theoretical information like some very specific description of the phenomenon under study and the equations used to execute the simulation. Generally space is not enough on the screen to show all this, then an information window is displayed on the click of a button.

Left : Ball - Wedge Elastic Collision.   The user sets ball velocity, ball and block mass, the program makes the simulation. As in all of these simulators slow motion and sound are at user's will.

Left: The Ballistic pendulum.-   The user controls bullet mass and velocity as well as block altitude.  A mouse click starts the simulation which may be visualized even in slow motion if the user wants.  

Cannon-Bullet and Falling-Mass Encounter.-

The user controls the cannon elevation angle, the bullet initial velocity and the horizontal distance from the cannon to the vertical along which the mass falls down since the moment the cannon makes fire.

The software calculates the corresponding mass-releasing altitude so that the bullet hits the falling mass. 

In the figure several cases are shown, each with a different color.

Bi Convex (Converging) Lens

The user sets the object distance to the lens and its size, the software computes the generated image size, position and other magnitudes and generates the corresponding visualization.


All  PVL  modules include theory, equations and relevant information.

Forces acting on a hanging picture. 

With the mouse the user places the picture wherever he wants on screen, all the involved forces appear automatically.  The  user controls picture weight and position.

Lissajous Orbits (Motion in two dimensions).

The superposition of two perpendicular Simple Harmonic Motions generates the Lissajous Orbits.  Freeze time at any moment to see why a central force is the resultant of the combined forces of two oscillating springs.  In this case the tracks of up to four experiments may be conserved on screen together with their generating parameters. The user sets the  Amplitudes, frequencies and initial phases of the oscillators.


The module dealing with Tri-Dimensional Lissajous shows the motion of Lissajous orbits in three dimensions. 

Light Refraction Through Stratified Media (10 slabs)

The user sets the refraction index of each of the slabs and the module makes the computations and shows the light trajectory through the slabs

Light refraction through a semi circular slab

The user sets the refraction index of the semi circular slab and with the mouse sets the angle of the incident ray, the module shows the correspondent reflected and refracted rays


Prices (US dollars) >>> PVL:  personal use:  100.00  --------------  Institutional use: 450.00 (Quantity discounts)                  

   Order online  - Downloads                                                      Back to Table of Contents     

"Physics Virtual Laboratory" and "Physics Virtual Lab" and "Laboratorio Virtual de Fisica" are registered trade names and trademarks, all rights are reserved.   

    List of  the  191  simulation modules of the Physics Virtual Lab ( PVL )

  Mechanics ( 82 ).-
1 Vectors: Addition, Difference, Scalar (Dot) product, Angle
2 Vector calculator:   Escalar product, Vector product, Triple product
3 Forces.- Components of a Pulling Force Applied to a Block
4             Resultant of the Forces acting on a Point .
5             Coplanar concurrent forces  
6             Equilibrium: Block on a surface: inclined and horizontal surfaces,
7             Equilibrium weighted horizontal bar resting on two supports
8             Car crossing a Bridge: Supporting Forces Evolution in a Two-Column Bridge
9             Forces on a Hanging Picture (Force needed to keep picture in any position)
10             Tension in the two ropes supporting a hanging block, Equilibrium
11             Forces in the ropes holding a hanging mass. Application of The Sine Law  
12             Coplanar Forces: Line of Action of Coplanar Forces
13             The Torque
14             Force and Torque Applied to a Wheel, direction of rotation
15             Equilibrium in a pivoted weighted slab - The seesaw
16             Two Blocks Hanging from the extremes of a Rope over a Pulley: Accelerations, Tensions
17 Friction.- Static and Kinetic Friction: Truck Pulling a Block Initially at Rest
18                     Block on a tilted plane: Static Friction Coefficient
19                     Rolling Friction
20 Rectilinear Motion:  Analysis of Position vs time graphs
21                            Under Constant Acceleration: Analysis of Velocity Graphs
22                            Under Constant Acceleration: Velocity and Position Graphs
23 Parabolic Motion.- Cannon: The Projectile Flight.
24                Cannon: Projectile flight with air resistance
25                Cannon projectile - External Ballistics
26                Parabolic Motion Velocities Analyzer
27                The Bombardier Drops a Bomb (parabolic motion of a bomb dropped from an airplane)
28                Cannon Bullet Hits Falling Mass
29                Pistol shooting velocity
30                Antiaircraft Fire Safety Zone
31                Cannon Shooting from an Elevated Position
32                Flight of a projectile vertically shot from a horizontally displacing car
33                Parabolic fall:  Velocity and Force Vectors
34                Projectile shot up an incline by a cannon
35 Curvilinear Motion:    Vectors of Velocity and Centripetal Force
36 Uniformly Accelerated Motion Data Plots Generator:  X(t), V(t), Delta X, V(x)
37 Falling Bodies.- Free Fall (vertical distances traveled by falling bodies are not constant)
38                      Parabolic vs. Vertical Trajectories of Falling bodies
39                      Crossing of parabolic and vertical falls
40 Mass Falling Down in a Medium whose Resistance is proportional to Velocity
41 Motion Against a Resistance Proportional to V ²  (squared velocity) 
42 Circular Motion.- Velocity and Acceleration Vectors
43                Linear Velocity vs. Angular Velocity
44                Tangential gear of wheels
45                Mixed Gearing of Wheels
46                Wheel rolling without slipping over the outer edge of a fixed circular ring
47                Wheel rolling without slipping over the inner edge of a fixed circular ring
48                Tangent Escape from a Circular Orbit.
49                Ball Bearing
50 Types of wheel motion
51 Motion in a vertical circular orbit
52 Two Concentric and Engaged Pulleys
53 Planet Motion (Energy and orbit size, Angular Moment and orbit shape)
54 Center of Mass (computes the CM of any number of particles of any mass).
55 Center of Mass behavior.
56 Gravitational Potential Energy Curves.
57 Energy:   Sliding on an Energy Bowl: Conservation of Kinetic and Potential Energies
58                   Rolling on an Energy Bowl
59                   Energy Conservation:   Looping the Loop.
60                   Energy Transformation:    Elastic - Kinetic - Potential
61                   Energy Transformation (Back & Forth): Potential (Elastic) - Kinetic - Potential (Gravitational) 
62                   Mechanical Energy Conservation: Ball falling and bouncing on a Spring
63                   Energy Transformation: Compressed Spring shoots a ball to the top of a bell-shaped hill.
64 Momentum.  Linear Momentum Conservation: The Air Track experiment
65                 Ball sliding over a curved track made on an unhampered car
66                 The Ballistic Pendulum (A bullet hits a hanging wooden block and this rises a certain height)
67 Angular Momentum Conservation
68 Collisions.- Bouncing Ball (Coefficient of restitution).
69                 Ball - Triangular Block
70                 Dispersion
71                 Inelastic Collision at a Crossroad
72                 Completely Inelastic Frontal Collision
73                 Completely Elastic Frontal Collision
74                 Coefficient of Restitution 
75 Sliding vs. Rolling on a tilted surface
76 The Two-Body System (rotation and displacement)  
77 Uniform Translational Relative Motion:  The Galileo Transform
78 Parabolic Motion - Problem Generator
79 Spring shoots block to pendulum
80 Pulley holding a block
81 Pendulum hits block on pedestal
82 Pulley System





Waves and Oscillations ( 39 ) .-        

1 Wave Motion ( Amplitude, Velocity, frequency, Wavelength)
2 Wave Motion direction
3 Hooke's Law
4 The Vibrator
5 Simple Harmonic Motion (SHM): The Rotor
6 SHM: Oscillating Spring
7 SHM: Oscillating spring:  Graphs of  x(t), v(t)  and a(t)
8 SHM: Graphs of  x(t), v(t), a(t)  and Acceleration vs Displacement
9 SHM: Energy Distribution in the Oscillating Spring
10 SHM: The Oscillating Block - Total Energy Distribution
11 SHM: Simple Harmonic Motion versus Non SHM
12 SHM: Superposition of three SHM in the same direction
13 SHM: The SHM - UCM  Connection
14 SHM: Superposition of two perpendicular SHM - Lissajous
15 SHM: Genesis of the Lissajous Figures
16 SHM: Variable-Phase-Difference Lissajous Figures
17 SHM: Superposition of three perpendicular SHM
18 SHM: The Oscillating Piston: Oscillation but not with SHM
19 SHM: Simple Pendulum executing a SHM
20 SHM: Addition of same-direction SHM oscillations
21 Physical Pendulum
22 Standing (Stationary) Waves
23 Damped traveling wave
24 Oscillations in a string fixed at both extremes
25 The Simple (Mathematical) Pendulum
26 Evolution of the forces acting on an oscillating pendulum
27 The Damped Oscillator
28 Damped Harmonic Oscillations Analyzer
29 Transverse Waves (ball on sea waves)
30 Longitudinal Waves

Analysis of traveling waves superposition

32 Superposition of up to Seven Traveling Waves
33 The Doppler Effect (Shock Waves)
34 Free Oscillator Phase-Space
35 Damped Oscillator Phase-Space
36 Damped Non-Linear Oscillator
37 Oscillations in a stretched rectangular membrane
38 Coupled pendulums.
39 Detection of damping by means of Logarithmic Decrement.
  Electricity and Magnetism ( 25 ).- 
1. Charging a Metal Sphere by Induction.
2. Charging two metal spheres by induction: opposite charges.
3. Electric Fields.-  E.F. due to unit charges (any number in any disposition)
4.                              Deflection of a Charged Particle traversing an E.F.  
5.                              E.F. and electric potentials due to point charges (any number, any position)
6. Electric field of an Oscillating Electric Dipole
7. Electric Circuit.-  Ohm’s Law
8.                              E.C. in Series (internal resistance)
9.                              E.C. in Parallel (internal resistance)

                             E.C. and dissipated power 1  (dissipated power in resistors)

11.                              E.C. and dissipated power 2 (dissipated power in resistors)  
12.                              Wheatstone Bridge
13.                              Slidewire Bridge Circuit
14.                              Voltmeter Bridge (between two parallel pairs of two resistors in series)
15.                              E. Current crossing the Bridge (between two parallel pairs of two resistors in series)
16. Magnetic Field .- Deflection of a Charged Particle traversing a M.F.  
17.                               Induced Emf by a variable M.F. flux on a square loop.
18.                               The Electric Transformer (Power, Voltages, Spire numbers, Currents)
19. Vector Field Flux
20. Alternating current (AC) generator, Rotating Spire.
21. Charged particles deflection in  E & B  fields.
22. Electromagnetic Wave .-  Time and Space Periodicity of the Harmonic EMW 
23.                                             EM wave front polarization (Linear, Circular, Elliptic).
244 Cherenkov Radiation
25. Oscillating Square Electric Quadrupole


  Thermodynamics ( 06 ).-
1. Temperature scales (Equivalence between Celsius, Kelvin, Fahrenheit and Rankine)
2. Boyle's law: Isotherms
3. Adiabatic expansion - compression of an ideal gas
4. The Carnot Engine.
5. The Piston Motor (four stage motor)  
6. Ideal and Real Gases Isothermal Compression.



  Propagation of Light - Optics - Color Theory ( 23 ).-
1 Color (RGB) Synthesis
2 Red, Green and Blue Color Mixing and Analysis
3 Snell's Law (Reflection and Refraction)
4 Semi-Circular Refraction Plate
5 Refraction:  Apparent Depth of Submerged Objects
6 Total Internal Reflection - Critical Angle
7 Doubly reflected light ray on an angular mirror
8 Total Reflection Prism
9 Refraction and Reflection
10 Bi-Convex (Convergent) Lens
11 Bi-Concave (Divergent) lens

Refraction through Parallel Plates

13 Refraction at a Plane Surface (Paraxial rays)
14 Flat Refracting Surface
15 Deviation by a Prism (Monochromatic ray)
16 Refracting Sphere (Monochromatic ray)
17 Rainbow origin:  Dispersion of white light in a raindrop
18 Spherical Aberration in a Concave Mirror
19 Convex Spherical Mirror
20 Concave Spherical Mirror

Young's Interference Experiment

22 Circular waves interference
23 Parabolic Antenna 



  Hydrostatics and Hydrodynamics ( 12 ).-
1. Pascal's law, The car lift  
2. Surface tension: air flowing between two bubbles connected by a pipe .
3. Water escaping from a hole or two holes in the wall of a tank.  
4. Leak through a tilted hole in a tank
5. Archimedes’ Principle  
6. Buoyant Force
7. Fictitious Weight on a bascule
8. Forces on the hull of a yacht
9. Viscous flow: Parabolic profile depending on pressures and on viscosity coefficient.  
10. Liquid speedometer  1  (Venturi meter)
11. Liquid speedometer  2  (Venturi meter)
12. U-Tube Venturi Speedometer


  Computer Games based on Mathematical Physics Modeling ( 04 )
1 Hit the tank from a flying bombardier
2 Shootdown with an antiaircraft cannon
3 Shoot down the UFO with an antiaircraft cannon
4 Bouncings 5


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 Chaos, Percolation, Stochastic Aggregation

Special Topics Simulation Software

Research Software

As a university professor, Javier Montenegro Joo (JMJ) carries out research and development with the aid of computers. In Physics, the research work of JMJ is mainly based on mathematical modeling and computer simulations. In Artificial Intelligence, the works of JMJ are on research and development of Digital Image Processing algorithms for Pattern Recognition.

Here some screen shots of the research works developed by Prof. Montenegro Joo are shown. Usually the results of the JMJ's works are  published in some specialized journals.

Stochastic aggregation of diffusing particles.

In this case diffusing (random displacing) particles stick around a unique cell usually placed at the center of coordinates. The aggregate shown here has 37153 particles, which may displace and stick to the aggregate following different rules imposed by the researcher.

The different colors indicate the order of arrival of the diffusing particles to the growing object, which generally is a fractal (it has statistical self-similarity). The resulting object has cavities because arriving particles cannot get into the inner regions of the aggregate. During research, the growing of aggregates with several millions of particles are computer simulated.

Site Percolation in the Square Lattice. 

Percolation phenomena deal with the propagation of information.  It is studied by means of Monte Carlo computer simulation, where the information travels from one extreme to the other in a lattice, that may be squared, hexagonal, etc., and the information propagates following different rules.

Percolation might be modeled as the propagation of a fire in a forest of trees. A burning tree passes fire to its neighboring trees.

At the beginning, there are randomly planted trees in a forest, then the first row of trees gets fire and these trees propagate the fire to their neighboring trees.   It has been encountered that for percolation to take place in a square net, the number of planted trees must be about 60%  of the available places.  Percolation is achieved as soon as the fire crosses the forest. 

  At research time much larger percolation networks are used.

Chemical Waves Simulator 

This Cellular Automata based simulator generates oscillation geometrical patterns similar to those observed in the Belusov-Zhabotinsky chemical reaction.


When the author of this web page was a child he used to pay with an elementary Chemistry Set. Combining several reactives in a glass with water, geometrical patterns of bubbles showed up at the surface of the water, and they repeated after some time, this is, those patterns had a Period.  Unfortunately neither the reactives nor their proportions were registered.


Chaos in a Non-Linear Damped & Periodically Forced Oscillator (NLDFO)

Below: One of the several Bifurcation Cascades (Chaotic events) resulting in a numerical simulation with the Runge-Kutta method on the differential equation modeling the system. 

Right:  The corresponding Return Map

As it can be appreciated, these plottings are plenty of tiny interesting details. Original plottings are much more larger, they have been reduced but trying to keep details visible.



Bifurcation cascades of a Chaotic event in the nonlinear damped and forced oscillator (NLDFO) obtained by numerical simulation.
A Poincare Map may be visualized as a tomographic cut at a certain angle in the State Space and, theoretically there may be an infinity of these tomographic cuts.
This plotting shows the peaks and valleys of the displacement.  Upper cascade:  Peaks = Poincare Map at 0°.   Lower cascade:  Valleys = Poincare Map at 180°.
Each chaotic event has a particular State Space, hence different chaotic events have different bifurcation cascades.
It can be seen that the system initially oscillates with a single period, which some time later bifurcates and the system oscillated with two periods, then with four, etc.
At the end of the chaotic event the system collapses its periods and it returns to its forced oscillations.

Variety and finiteness of Chaotic Events

JMJ has developed a VirtualLab which has detected several chaotic events in the non-linear damped and periodically forced oscillator (NLDFO). The image at the left displays some chaotic events with the corresponding number of time-steps in the simulation.   After finding several chaotic events in the NLDFO, it is natural to expect that other chaotic systems show also a variety of chaotic occurrences. Notice that the detected chaotic events have a beginning and an end, this is, chaotic events are transitory (limited in time)

Not all systems prone to chaos evolve towards chaos through a cascade of period bifurcations, like the oscillator shown here (NLDFO) does. Investigating the transition to chaos in both, the Van der Pol  and  the Duffing oscillators, JMJ has observed no cascade of bifurcations, only a weird behavior   in Phase Space.

Our hearts are nonlinear forced oscillators

In real life systems are mostly non-linear, and there are oscillating systems everywhere, even the heart is an oscillator (it oscillates between diastole and systole), it is non-linear, it is damped (by the viscosity of the blood) and it is forced (because it is the brain who stipulates its rhythm of oscillation). Notwithstanding the equation used in this simulation IS NOT a model of the oscillations of the heart, studying its transition to chaos gives an idea of the heart fibrillation before its collapse.

Notice that chaotic events eventually terminate, hence if machines (and our hearts) were able to experience and overcome a chaotic event then we would be beholding self-repairing machines and persons that survive a (very strong) heart attack.

Unhappily neither persons nor machines are prepared to get through a chaotic event, hence persons die and machines become out of order.

It is a common experience that when a machine starts to behave weird, it repairs itself after a hand blow or a kick (when the machine is rather big). Physicians recommend escaping from an incipient heart attack by coughing very strongly. It may be that in cases like these, as a result of coughing or hitting, the system jumps to the end of the chaotic event and thus it gets to escape from that.

Bifurcation cascades of extreme velocities in the chaotic NLDF Oscillator:

Evolution of the velocity during a chaotic event in the nonlinear damped and forced oscillator (NLDFO). This two graphs show the extreme values of the velocity in the NLDFO, these are obtained extracting the Poincaré Maps at 90° and 270° , respectively. A Poincaré Map is a tomographic cut along the State Space of the chaotic event. It can be seen that the velocity also bifurcates during a chaotic event.  These results shed light on the behavior of other chaotic systems.

Would you like to know more about Chaos ?      Download my latest research papers ...




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Audio Visualizer


AudioVisualizer:  Ultra Quick Audio Visual File Explorer  

Very useful ultra quick Audio Visual File Explorer dealing strictly with the most commonly used file formats (this is why it is ultra quick), permits to very quickly and with only a single mouse click visualize (or listen to) hundreds of images and files containing textual information, also explores by executing animated-Gif images,  audio (sound) and video  files.
Very quickly can explore hundreds of sound, image and textual files.  Useful when the user wants to very quickly get to know the contents of many files (text, sound, images, video) in a very short time. There is absolutely no waiting when shifting files.

Supported File formats... Image Files: Bmp, Jpg, Gif, Ico, Emf, Wmf, Animated Gif. Video Files: Avi. Sound Files: Wav, Mid.  
Exe-type files are executed.  All other file formats ( .pas, .cpp, .dsk, etc, etc) are displayed as .txt 
Files may be deleted, renamed, and printed.                                                         

AudioVisualizer ---- Price  US dollars:  35.00  

   Order online - Downloads                 Back to Table of Contents            Download   AudioVisualizer Demo    



Minimum System Requirements:  

All the software exposed in this web page can be executed ( works ) in a  Personal Computer  that has  AT LEAST  the following features: 

Obviously, the software also executes (works) in a  PC  with more advanced description.

Upgrades At No Extra Cost ....

If you are a user of  VirtualDynamicsSoft software and see in this web page that the software you are using has

now a new version (upgrade or more simulators), please send e-mail to  Updates@VirtualDynamicsSoft.com   

requesting a free update / upgrade,  this will be immediately sent to you via e.mail as an attached file.


Easy Ordering Information and Downloads


<><><><><> Order Online: Buying in Shareit, the worldwide internet Software market

Paying with Credit Cards (including Pay Pal)


 Receiving the Virtual Lab of your choice ....

In order to buy and receive the Virtual Lab of your choice (through a download link or via email as an attached file) click  the corresponding link below. 

Email the author if you have problems.  VirtualDynamicsSoft  also sends the software you order  via e-mail as an attached file.


Worldwide  EduVirtualLabs  distribution by Share-it    ( Germany )
CurvilinearS  (version en Español)            ID-Number in Shareit :  145981
CurvilinearE  (English version)           ID-Number in Shareit : 146043 
 Panageos (English version)             ID-Number in Shareit : 146044
Easy TOEFL Grammar  (English version)            ID-Number in Shareit : 146246
Imagery (Digital Image processing EduVirtualLab)           ID-Number in Shareit :  300498500   


AudioVisualizer     (English version)         ID-Number in Shareit : 150477
07 PVL, Physics Virtual Lab     (Institutional version, English version)          ID-Number in Shareit:  300120665
PVL, Physics Virtual Lab     (Individual version, English version)         ID-Number in Shareit:  152786
09 Mathematics Virtual Lab      (MVL,  Institutional Version)       ID-Number in Shareit: 300399018


10 Mathematics Virtual Lab      (MVL, Individual version, English version)         ID-Number in Shareit:   164448
EconoModeler (English version)                 ID-Number in Shareit: 203464

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