Related papers: A non-standard approach to introduce simple harmon…
We derive the non-linear semiclassical equation of motion for a general diffeomorphism-invariant theory of gravity by leveraging the thermodynamic properties of closed causal horizons. Our work employs two complementary approaches. The…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
In this paper an asymptotic solution of the spherical harmonics equations describing the charge transport in semiconductors is found. This solution is compared with a numerical solution for bulk silicon device. We also indicate application…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…
(Talk presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford, CA, July 24-30, 1994) We study the semi-classical limit of the solution of the Dirac equation in a background electromagnetic/gravitational plane wave. We…
In the one-loop approximation we derive the equation of motion for a classical scalar field \phi_c (t) with the back reaction of particle production included. Renormalization of mass and couplings of \phi_c is done explicitly. The equation…
The object of this work is the numerical investigation of a non-commutative field theory defined via the spectral action principle. The Starting point is a spectral triple (A,H,D) referred to as harmonic. The construction of these data…
The Self-Consistent Harmonic Approximation (SCHA) has been utilized to investigate quantum and thermal phase transitions within magnetic models and, more recently, in spintronic applications. The SCHA methodology involves utilizing simple…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
A simple procedure for restoring the constants in physical equations is introduced by a consistent consideration of the correspondence between the symbols representing physical quantities and pairs formed by numerical values and unit…
The compatibility of standard and Bohmian quantum mechanics has recently been challenged in the context of two-particle interference, both from a theoretical and an experimental point of view. We analyze different setups proposed and derive…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…