The EJS 2D Ising model displays a lattice of spins. You can change the lattice size, temperature, and external magnetic field. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. The 2D-Ising model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_stp_Ising2D.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Advanced Mathematical Models & Applications (ISSN 2519-4445) is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues. The language of the journal is English.

Students explore Hooke's law while working in small groups at their lab benches. They collect displacement data for springs with unknown spring constants, k, by adding various masses of known weight. After exploring Hooke's law and answering a series of application questions, students apply their new understanding to explore a tissue of known surface area. Students then use the necessary relationships to depict a cancerous tumor amidst normal tissue by creating a graph in Microsoft Excel.

The Chemical Potentials by Monte Carlo Simulations Model performs canonical (NVT) and isothermal-isobaric (NPT) Monte Carlo simulations focusing the calculation of chemical potentials, for the fluid phases of the Lennard-Jones system, by using the virtual particle insertion method of Widom. Although it can not determine phase-equilibrium directly, the gas-liquid line can be approached as illustrated in the included case study. The model paves the way to uVT and Gibbs Ensemble simulations, and shows the limitation of Widom's method at high fluid densities. The Chemical Potentials by Monte Carlo Simulations Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

This interactive, scaffolded activity allows students to build an atom within the framework of a newer orbital model. It opens with an explanation of why the Bohr model is incorrect and provides an analogy for understanding orbitals that is simple enough for grades 8-9. As the activity progresses, students build atoms and ions by adding or removing protons, electrons, and neutrons. As changes are made, the model displays the atomic number, net charge, and isotope symbol. Try the "Add an Electron" page to build electrons around a boron nucleus and see how electrons align from lower-to-higher energy. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology. The Concord Consortium develops deeply digital learning innovations for science, mathematics, and engineering. The models are all freely accessible. Users may register for additional free access to capture data and store student work products.

This interactive activity helps learners visualize the role of electrons in the formation of ionic and covalent chemical bonds. Students explore different types of chemical bonds by first viewing a single hydrogen atom in an electric field model. Next, students use sliders to change the electronegativity between two atoms -- a model to help them understand why some atoms are attracted. Finally, students experiment in making their own models: non-polar covalent, polar covalent, and ionic bonds. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology.

This concept-building activity contains a set of sequenced simulations for investigating how atoms can be excited to give off radiation (photons). Students explore 3-dimensional models to learn about the nature of photons as "wave packets" of light, how photons are emitted, and the connection between an atom's electron configuration and how it absorbs light. Registered users are able to use free data capture tools to take snapshots, drag thumbnails, and submit responses. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology.

The Confined Hard Disk Two Piston System simulates a constant-energy two-dimensional system of unit mass particles confined by two frictionless pistons of equal mass M. This computer model complements theoretical work describing the adiabatic expansion of an ideal gas using the quasi-static approximation. Users can set the number of particles N, their diameter and their initial particle kinetic energy. Slow-moving particles are color-coded as blue and fast particles are color-coded as yellow. The time evolution of temperature, pressure, and piston speed are shown in a second window.   Particles in this model have unit mass and interact through contact forces. Collision times are computed analytically because particles and pistons move with constant velocity between collisions. The time evolution algorithm advances the particle position from collision to collision until the requested time step is achieved. The time evolution is then paused, data is accumulated, and the screen is redrawn. The Confined Hard Disk Two Piston System was developed using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_stp_hd_ConfinedHardDiskTwoPistonSystem.jar file will run the program if Java is installed.

The Confined Lennard-Jones System is an idealized statistical mechanics model that simulates a two-dimensional system of particles confined to a box with a constant temperature thermal reservoir at one end and a movable piston at the other. Particles in this model have unit mass and interact through pairwise Lennard-Jones forces and hard-wall contact forces. Slow-moving particles are color-coded as blue and fast particles are color-coded as yellow. The model computes and plots the evolution of the total energy E, the kinetic energy per particle K, the pressure P, and the volume V. The model also displays histograms and mean values of these quantities. The Confined Lennard-Jones System was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_stp_md_ConfinedLennardJonesSystem.jar file will run the program if Java is installed.

The Confined Lennard-Jones Two Piston System simulates a constant-energy two-dimensional system of particles confined by two frictionless pistons of equal mass M. This computer model complements theoretical work describing the adiabatic expansion of an ideal gas using the quasi-static approximation. Users can set the initial particle kinetic energy, Lennard Jones parameters, and the initial particle separation. Slow-moving particles are color-coded as blue and fast particles are color-coded as yellow. The time evolution of temperature, pressure, and piston speed are shown in a second window. Particles in this model have unit mass and interact through pairwise Lennard-Jones forces and hard-wall contact forces. The instantaneous temperature is computed using the average particle kinetic energy and the pressure is computed using the virial expansion. The Confined Lennard-Jones Two Piston System is a supplemental simulation for the article "Evolution of ideal gas mixtures confined in an insulated container by two identical pistons" by Joaquim Anacleto, Joaquim Alberto C. Anacleto, and J. M. Ferreira in the American Journal of Physics 79(10), 1009-1014 (2011) and has been approved by the authors and the American Journal of Physics (AJP) editor. The Confined Lennard-Jones Two Piston System was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_stp_md_ConfinedLennardJonesTwoPistonSystem.jar file will run the program if Java is installed.

This online interactive module of 10 pages or frames integrates textual information, 3D molecular models, interactive molecular simulations, and embedded assessment items to guide students in understanding the copying of DNA base sequences from translation to transcription into proteins within each cell. The module divides the exercises in to Day 1 and Day 2 time frames. Teachers can view student assessment responses by assigning the module within a class created within the Molecular Workbench application. This Java-based module must be downloaded to each computer.

Student groups are provided with a generic car base on which to design a device/enclosure to protect an egg on or in the car as it rolls down a ramp at increasing slopes. During this in-depth physics/science/technology activity, student teams design, build and test their creations to meet the design challenge, and are expected to perform basic mathematical calculations using collected data, including a summative cost to benefit ratio.

A set of simulations and accompanying worksheets have been developed as guided inquiry learning materials for upper division thermal physics. The content follows closely the approach taken by "An Introduction to Thermal Physics" by Daniel Schroeder.

A worksheet that considers an Einstein solid in contact with a temperature demon (a single oscillator thermometer that exchanges energy with the Einstein solid). The combined solid-demon system is isolated. The number of energy units in this system can be adjusted by editing the field in the main display. All of this energy is originally in the Einstein solid, but after interaction starts it is shared between the demon and the Einstein solid.

A worksheet that considers the case of an Einstein solid in thermal contact with a large reservoir or heat bath. Energy is continually exchanged between the bath and the solid, but the bath is so large that its temperature remains constant.

The Ejs Hard Disk Gas model displays a two-dimensional gas made out of hard disks. Particles are initialized with a speed v=1 in a random direction and move with constant velocity until a collision occurs. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Hard Disk Gas model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_newton_HardDiskGas.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for statistical mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

The Lennard-Jones Fluid 2D program shows a system of particles in two dimensions interacting via the Lennard-Jones potential. The program displays the particles in the box as a function of time once the partition dividing the box into three parts are removed. The program is distributed as a ready-to-run (compiled) Java archive. Double-clicking the ejs_stp_LJFluid2D.jar file will run the program if Java is installed on your computer. The program was created using Ejs (Easy Java Simulations). You can modify this program and see how it is designed if you have Ejs installed by right-clicking within the window and selecting Open Ejs Model from the pop-up menu. Ejs, a part of the Open Source Physics Project, is designed to make it easier to access, modify, and generate computer models. Information about Ejs is available at www.um.es/fem/Ejs/. Additional Open Source Physics programs for Statistical and Thermal Physics can be found by searching ComPADRE for Open Source Physics, STP or Statistical and Thermal Physics.

The Grand Canonical Monte Carlo Model illustrates grand canonical ensemble (µVT) Monte Carlo simulations: the chemical potential, volume and temperature are the system constraints. This means that the system has porous and diabatic walls, exchanging molecules and heat with a reservoir at constant chemical potential and temperature. The molecules interact through the Lennard-Jones. potential and fluid states at densities 0.0025 ? ? ? 0.85 and temperatures T ? 0.70 can be simulated. Although the volume is kept constant, the number of molecules fluctuates and so does the density. The aim is to reach a chemical potential approaching the imposed one. The input fields can be edited to probe different regions of the phase diagram. Chemical potentials, activity coefficients, Helmholtz free energies, entropies and their excess contributions are worked out. The Grand Canonical Monte Carlo Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

In this activity, students work in teams to construct the components of the model and make presentations on the results of their effort.

The HS-WCA-LJ Monte Carlo Model performs simultaneous canonical Monte Carlo (MC) simulations of 108, 256 or 500 particles interacting through the hard sphere (HS), the Weeks, Chandler and Andersen (WCA) and the Lennard-Jones (LJ) pair potentials. It was inspired by the review of Chandler, Weeks and Anderson on WCA theory, illustrating that "the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces". The radial distribution functions for the three systems are plotted after every MC cycle, at densities and temperatures chosen by the user, and the data Tables display thermodynamic results from the LJ and WCA potentials. The thermodynamics of the HS system was addressed to another application cataloged at Open Source Physics. The objective of this application is: (i) to illustrate the canonical MC method with three different systems;(ii) to probe the densities and temperatures at which the HS and WCA potentials approach the structure(defined by the radial distribution functions) of the LJ system, regarding their use in perturbation theory. The HS-WCA-LJ Monte Carlo Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.