Related papers: Determining the full transformation relations in t…
This study focuses on linear partial differential equation (PDE) systems that arise in topology optimization where the thickness of a structure is constrained. The thickness derived from the PDE is a fictitious one, and the key challenge of…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine…
In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns \theta (absolute temperature), u (displacement), and…
We represent an integration algorithm combining the characteristics method and Hopf-Cole transformation. This algorithm allows one to partially integrate a large class of multidimensional systems of nonlinear Partial Differential Equations…
We present here a short and subjective review of methods for calculating charge transfer couplings. Although we mostly focus on Density Functional Theory, we discuss a small subset of semiempirical methods as well as the…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation…