Related papers: Variational formulation and efficient implementati…
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…
Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final state interactions. A…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
In modeling relativistic thermodynamics, we frequently regard the particle number as a conserved quantity. The number conservation law, which comes from the requirement that the pull-back construction from fluid-matter 3-space has the same…
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a uniform parabolicity condition. As the main…
In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity.…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…
A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered…
In this paper, Newton's law of cooling is considered from a different perspective with newly defined fractional conformable. Obtained results are compared with experimental results and found optimal fractional orders which fit better with…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm)…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…