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We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
We expand the classic variational formulation of $-\log\mathbb{E}\left[e^{-f}\right]$ to the case where f depends on a diffusion, and not only a on Brownian motion, while decreasing the integrability hypothesis on f. We also give an…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
Survival regression is widely used to model time-to-events data, to explore how covariates may influence the occurrence of events. Modern datasets often encompass a vast number of covariates across many subjects, with only a subset of the…
The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range.…
The set of closed (or holonomic) measures provides a useful setting for studying optimization problems because it contains all curves, while also enjoying good compactness and convexity properties. We study the way to do variational…
The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought,…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…
Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly…
This work presents an analytical and computational study of fractional-order delay differential equations formulated using both the conformable and Caputo derivatives. For the conformable case, we develop the associated integral,…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
Time series data are often obtained only within a limited time range due to interruptions during observation process. To classify such partial time series, we need to account for 1) the variable-length data drawn from 2) different…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…
The problem of exponentiating derivations of quasi *-algebras is considered in view of applying it to the determination of the time evolution of a physical system. The particular case where observables constitute a proper CQ*-algebra is…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
When designing and developing scale selection mechanisms for generating hypotheses about characteristic scales in signals, it is essential that the selected scale levels reflect the extent of the underlying structures in the signal. This…