Related papers: myPhysmatics: Connected Mathematical Models in Phy…
The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…
Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential…
Throughout life, we might seek a calling, companions, skills, entertainment, truth, self-knowledge, beauty, and edification. The practice of curiosity can be viewed as an extended and open-ended search for valuable information with hidden…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
This paper attempts to review our studies on the propagation of signals in nerves over the past decade. The need for interdisciplinary studies is stressed that helps to understand the physical mechanisms of coupling the electrical,…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
Understanding the causes and consequences of, and devising countermeasures to, global warming is a profoundly complex problem. Network representations are sometimes the only way forward, and sometimes able to reduce the complexity of the…
Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…
Finding patterns in data is one of the most challenging open questions in information science. The number of possible relationships scales combinatorially with the size of the dataset, overwhelming the exponential increase in availability…
Single particle models are sufficient for many topics in introductory physics courses, but become misleading when applied to situations involving changes in internal energy. This paper merges two parallel attempts to reform the teaching of…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…