Related papers: Path integral approach to random motion with nonli…
In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D_I and D_II, respectively. On D_I there are three and on D_II…
We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising $p$-spin glass model, and (b)…
We define and investigate the properties of the jaggedness of path integral trajectories. The new quantity is shown to be scale invariant and to satisfy a self-averaging property. Jaggedness allows for a classification of path integral…
Conventional rendering techniques are primarily designed and optimized for single-frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
The formulation of the relativistic spinless path integral on the general affine space is presented. For the one dimensional space, the Duru-Kleinert (DK) method and the $\delta $-function perturbation technique are applied to solve the…
This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path…
A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…