Open Access. Powered by Scholars. Published by Universities.®
Statistical, Nonlinear, and Soft Matter Physics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Applied Mathematics (4)
- Dynamic Systems (2)
- Other Physics (2)
- Biochemistry, Biophysics, and Structural Biology (1)
- Biophysics (1)
-
- Cell Biology (1)
- Cell and Developmental Biology (1)
- Computer Sciences (1)
- Diseases (1)
- Fluid Dynamics (1)
- Life Sciences (1)
- Medicine and Health Sciences (1)
- Non-linear Dynamics (1)
- Numerical Analysis and Computation (1)
- Ordinary Differential Equations and Applied Dynamics (1)
- Other Applied Mathematics (1)
- Parasitic Diseases (1)
- Partial Differential Equations (1)
Articles 1 - 5 of 5
Full-Text Articles in Statistical, Nonlinear, and Soft Matter Physics
Probing The Ising Model’S Thermodynamics Through Restricted Boltzmann Machines, Xiaobei (Emma) Zhang
Probing The Ising Model’S Thermodynamics Through Restricted Boltzmann Machines, Xiaobei (Emma) Zhang
HMC Senior Theses
This thesis explores the connection between physics and machine learning by using Restricted Boltzmann Machines (RBMs) to study the thermodynamic properties of the Ising model. The Ising model is a simple but realistic model that captures the magnetic behavior of a system, where spins occupy a lattice of sites and different spin configurations correspond to different energies. The model exhibits phase transitions between ferromagnetic and paramagnetic phases as a function of temperature. RBMs are two-layered neural networks that can learn probability distributions over binary spins. The study generates 2D Ising model data at different temperatures using Monte Carlo simulations, including …
Giardia Lamblia Growth In Viscoelastic Fluids, Kelly Watanabe
Giardia Lamblia Growth In Viscoelastic Fluids, Kelly Watanabe
CMC Senior Theses
Giardia lamblia is a single-celled protozoan parasite that when ingested, causes diarrheal disease and infects 33% of people in developing countries. Previous studies observe Giardia in water-like fluids, but Giardia's infectious environment consists of viscoelastic mucus in the small intestine. Therefore, Giardia was cultured in viscoelastic fluids, and its population growth was observed in vitro. To create shear-thinning viscoelastic fluids, 0.2% and 0.4% long-chain polyacrylamide (LCPAM) was added to cell culture media. Giardia was cultured in control media, 0.2% LCPAM, and 0.4% LCPAM, and population growth was quantitatively determined over time. Increasing LCPAM concentration resulted in a solution with …
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Scripps Senior Theses
Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime, Weerapat Pittayakanchit
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime, Weerapat Pittayakanchit
HMC Senior Theses
Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single …
Energy-Driven Pattern Formation In Planar Dipole-Dipole Systems, Jaron P. Kent-Dobias
Energy-Driven Pattern Formation In Planar Dipole-Dipole Systems, Jaron P. Kent-Dobias
HMC Senior Theses
A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The com- petition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant in the macroscopic limit and contribute only to a constant offset in the system’s energy. A numeric model is developed, and some important stable domain morphologies are characterized. Previously unresolved bifurcating branches are explored. Finally, by applying a random energy background to …