Related papers: V-shaped action functional with delay
The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an…
We investigate vapor-liquid phase separation of an active near critical Lennard-Jones fluid confined within a cylindrical pore using molecular dynamics simulations. Activity is introduced via Vicsek-type alignment interactions, enabling a…
We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla…
We study the $L^2$-gradient flow of functionals $\mathcal F$ depending on the eigenvalues of Schr\"odinger potentials $V$ for a wide class of differential operators associated to closed, symmetric, and coercive bilinear forms, including the…
We develop a framework for studying consistent interactions of local gauge theories, which is based on the presymplectic BV-AKSZ formulation. The advantage of the proposed approach is that it operates in terms of finite-dimensional spaces…
This paper discusses a multi-term time-fractional delay differential equation in a real Hilbert space. An iterative scheme for a multi-term time-fractional differential equation is established using Rothe's method. The method of…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
The flux function in the Buckley-Leverett equation, that is, the function characterizing the ratio of the relative mobility functions of the two phases, is considered. The common conjecture stating that any convex mobilities result in an…
An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…
In this article we study the gradient flow equation of a variant of the Rabinowitz action functional on very negative line bundles and relate it to periodic orbits on the base of this bundle. On very negative line bundles there are…
We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally…
This paper reconsiders refinements which introduce actions on the concrete level which were not present at the abstract level. It draws a distinction between concrete actions which are "perspicuous" at the abstract level, and changes of…
The exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's…
A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…
We propose an alternative method for Feynman path integrals on compact Riemannian manifolds. Our method employs action integrals along the shortest paths. In the case of rank 1 locally symmetric Riemannian manifolds, we prove the strong…
A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate…
We consider a class of measures absolutely continuous with respect to the distribution of the stopped Wiener process $w(\cdot\wedge\tau)$. Multiple stochastic integrals, that lead to the analogue of the It\^o-Wiener expansions for such…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…