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We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…
The dynamics and thermal structure of the surface layers of stars with outer convection zones can be studied in some detail by means of numerical simulations of time-dependent compressible convection. In an effort to investigate the…
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose…
Doubly diffusive convection describes the fluid motion driven by the competition of temperature and salinity gradients diffusing at different rates. While the convective motions driven by these gradients usually occupy the entire domain,…
In this review we discuss the recent progress in the simulation of soft active matter systems and in particular the hydrodynamics of microswimmers using the method of multiparticle collision dynamics, which solves the hydrodynamic flows…
This work aims at generating a model of the ocean surface and its dynamics from one or more video cameras. The idea is to model wave patterns from video as a first step towards a larger system of photogrammetric monitoring of marine…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
Quantitative methods are more familiar to most geophysicists with direct inversion or indirect inversion. We will discuss seismic inversion in a high level sense without getting into the actual algorithms. We will stay with meta-equations…
The hydrodynamic performance of a sea-going ship can be analysed using the data obtained from the ship. Such data can be gathered from different sources, like onboard recorded in-service data, AIS data, and noon reports. Each of these…
In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces,…
A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of astrophysical objects. The theoretical…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
By virtue of Rayleigh-Benard convection, we illustrate the advantages of combining a hydrodynamic pattern forming instability with a thermodynamic critical point. This has already lead to many novel unexpected observations and is further…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the…
Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic…