A phase-field model is a mathematical model for solving interfacial problems. It has mainly been applied to solidification dynamics, but it has also been applied to other situations such as viscous fingering, fracture mechanics, hydrogen embrittlement, and vesicle dynamics. The method substitutes boundary conditions at the interface by a partial differential equation for the evolution of an auxiliary field (the phase field) that takes the role of an order parameter. This phase field takes two distinct values (for instance +1 and −1) in each of the phases, with a smooth change between both values in the zone around the interface, which is then diffuse with a finite width. A discrete location of the interface may be defined as the collection of all points where the phase field takes a certain value (e.g., 0). A phase-field model is usually constructed in such a way that in the limit of an infinitesimal interface width (the so-called sharp interface limit) the correct interfacial dynamics are recovered. This approach permits to solve the problem by integrating a set of partial differential equations for the whole system, thus avoiding the explicit treatment of the boundary conditions at the interface. Phase-field models were first introduced by Fix and Langer, and have experienced a growing interest in solidification and other areas. (Wikipedia).
Differential Equations: Direction Fields and the Phase Line
Direction fields are useful tools for visualizing the flow of solutions to differential equations. Unfortunately, drawing line segments and calculating their slopes at every point on a grid is painfully slow and boring. There are more efficient ways to sketch direction fields. In this vide
From playlist Differential Equations
Phase Portrait for Double Well Potential
No one can hear you scream in phase space. In this video we explore the phase portrait of a double-well potential system, which is a fun example of a nonlinear system (i.e., differential equation) that can be analyzed with local linearization and linear solution techniques. Playlist:
From playlist Engineering Math: Differential Equations and Dynamical Systems
(8.1.102) Creating Phase Portraits for Nonlinear Autonomous Systems of ODEs
This video explains how to use an online tool to create a phase portrait or phase diagram for given nonlinear system of differential equation. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Ryan Thorngren - Higher Berry Phase and Diabolical Points in Phase Diagrams of Many-body Systems
The Berry phase is a well-known phenomenon in quantum mechanics with many profound implications. It describes the response of the phase of the wavefunction to the adiabatic evolution of system parameters, defining a U(1) connection on the parameter space. In many-body systems described by
From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory
We discuss the use of Phase Plane Plots for understanding the qualitative behavior of systems of differential equations.
From playlist Mathematical Physics I Uploads
Bound-preserving numerical solutions of variable density two-phase flows
Date and Time: Thursday, November 11, 12:00pm Eastern time zone Speaker: Beatrice Riviere, Rice University Abstract: Modeling pore-scale flows modeling is important for many applications relevant to energy and environment. Phase-field models are popular models because they implicitly tra
From playlist SIAM Geosciences Webinar Series
Phase separation of oil and water, in a grid model
Following work by Eran Agmon et al.: http://mitpress.mit.edu/sites/default/files/titles/content/alife14/978-0-262-32621-6-ch082.pdf At every grid point there are two numbers, representing the concentration of oil and water respectively. We compute how these numbers should change based on
From playlist Ready
Young's double-slit experiment for a quantum particle, phase representation
Simulation of Schrödinger's equation for a quantum particle moving towards, and partly through, a double slit. This is the same evolution as in the video https://youtu.be/K-YDj2odL8I but with a different color scheme. Luminosity corresponds to the probability of finding the quantum particl
From playlist Schrödinger's equation
Phase separation in the Allen-Cahn equation, with a start in slow motion
Like the video https://youtu.be/t1swj0QJUTw this simulation shows a solution of the Allen-Cahn equation for phase separation, on a rectangular domain with periodic boundary conditions, starting from a random initial configuration. Time has been slowed down at the beginning, to give a bette
From playlist Reaction-diffusion equations
Simple models of Symmetry Protected Topological phases
Simple models of Symmetry Protected Topological phases and Symmetry Enriched Topological phases of bosons in two and three dimensions Discussion Meeting: Quantum entanglement in macroscopic matter URL: http://www.icts.res.in/discussion_meeting/QEM2015/ Dates: Monday 12 Jan, 2015 - Friday
From playlist Discussion Meeting: Quantum entanglement in macroscopic matter
Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry (1/4)
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019
From playlist Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry
Topology and Strong Four-fermion Interactions by Simon Catterall
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Partial deconfinement in large N gauge theory by Hiromasa Watanabe
PROGRAM: NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph
From playlist NUMSTRING 2022
2020 Theory Winter School: Srinivas Raghu
Topic: Boson-ferimon duality in strongly coupled field theories For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
Fractionalized fermionic quantum criticality by Lukas Janssen
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
Quantum Thermal Hall Effect of Chiral Spinons in a Kagome Strip by Efrat Shimshoni
DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r
From playlist Edge dynamics in topological phases 2019
Tensor network studies of SrCu2(BO3)2 by Philippe Corboz
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
Correlation induced metallic, half-metallic and superconducting by H. R. Krishnamurthy
DISCUSSION MEETING NOVEL PHASES OF QUANTUM MATTER ORGANIZERS: Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara DATE: 23 December 2019 to 02 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Recent theoretical and experimental
From playlist Novel Phases of Quantum Matter 2019
Phase Transitions in Random-field and Random-anisotropy Magnets by Sumedha
DISCUSSION MEETING STATISTICAL PHYSICS: RECENT ADVANCES AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Sakuntala Chatterjee (SNBNCBS, Kolkata), Kavita Jain (JNCASR, Bangalore) and Tridib Sadhu (TIFR, Mumbai) DATE: 14 February 2022 to 15 February 2022 VENUE: Online In the past few dec
From playlist Statistical Physics: Recent advances and Future directions (ONLINE) 2022