Related papers: On simplified models for dynamics of pointlike obj…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
This note is concerned with the problem of motion modeling in Physics. We aim to use the Time-Variant Local Autocorrelation Polynomial to understand the mathematical model of motion description. The mathematical explanation of the existence…
In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…
The ability to construct, use, and revise models is a crucial experimental physics skill. Many existing frameworks describe modeling in science education at introductory levels. However, most have limited applicability to the context of…
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models…
Evolution has resulted in highly developed abilities in many natural intelligences to quickly and accurately predict mechanical phenomena. Humans have successfully developed laws of physics to abstract and model such mechanical phenomena.…
We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
A new approach to model the biomatter dynamics based on the field theory is presented. It is shown that some well known tools in field theory can be utilized to describe the physical phenomena in life matters, in particular at elementary…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…
A definition of a {\it Realistic} Physics Theory is proposed based on the idea that, at all time, the set of physical properties possessed (at that time) by a system should unequivocally determine the probabilities of outcomes of all…
It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…