Time-Dependent Fluid-Structure Interaction

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure which reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM

Interaction corrections at intermediate temperatures: dephasing time

We calculate the temperature dependence of the weak localization correction in a two dimensional system at arbitrary relation between temperature, $T$ and the elastic mean free time. We describe the crossover in the dephasing time ${\tau_\phi(T)}$ between the high temperature, $1/\tau_\phi \simeq T^2 \ln T$, and the low temperature $1/\tau_\phi \simeq T$ behaviors. The prefactors in these dependences are not universal, but are determined by the Fermi liquid constant characterising the spin exchange interaction.Comment: 4 pages, to appear in PRB, minor errors corrected, added reference

Time scales and structures of wave interaction

In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in \emph{Kartashova, PRE \textbf{86}: 041129 (2012)} describing interactions of distinct modes. Applying time scale analysis to weakly nonlinear wave systems modeled by the focusing nonlinear Sch\"{o}dinger equation, we give an overview of the structures appearing in Wave Interaction Theory, their time scales and characteristic times. We demonstrate that kinetic cascade and D-cascade are not competing processes but rather two processes taking place at different time scales, at different characteristic levels of nonlinearity and due to different physical mechanisms. Taking surface water waves as an example we show that energy cascades in this system occur at much faster characteristic times than those required by the kinetic WTT but can be described as D-cascades. As D-model has no special pre-requisites, it may be rewarding to re-evaluate existing experiments in other wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc. To appear in EP

Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction

We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists $t_0>0$ such that the distribution at time $t\leq t_0$ is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics

A real-time human-robot interaction system based on gestures for assistive scenarios

Natural and intuitive human interaction with robotic systems is a key point to develop robots assisting people in an easy and effective way. In this paper, a Human Robot Interaction (HRI) system able to recognize gestures usually employed in human non-verbal communication is introduced, and an in-depth study of its usability is performed. The system deals with dynamic gestures such as waving or nodding which are recognized using a Dynamic Time Warping approach based on gesture specific features computed from depth maps. A static gesture consisting in pointing at an object is also recognized. The pointed location is then estimated in order to detect candidate objects the user may refer to. When the pointed object is unclear for the robot, a disambiguation procedure by means of either a verbal or gestural dialogue is performed. This skill would lead to the robot picking an object in behalf of the user, which could present difficulties to do it by itself. The overall system — which is composed by a NAO and Wifibot robots, a KinectTM v2 sensor and two laptops — is firstly evaluated in a structured lab setup. Then, a broad set of user tests has been completed, which allows to assess correct performance in terms of recognition rates, easiness of use and response times.Postprint (author's final draft

Dynamic Illumination for Augmented Reality with Real-Time Interaction

Current augmented and mixed reality systems suffer a lack of correct illumination modeling where the virtual objects render the same lighting condition as the real environment. While we are experiencing astonishing results from the entertainment industry in multiple media forms, the procedure is mostly accomplished offline. The illumination information extracted from the physical scene is used to interactively render the virtual objects which results in a more realistic output in real-time. In this paper, we present a method that detects the physical illumination with dynamic scene, then uses the extracted illumination to render the virtual objects added to the scene. The method has three steps that are assumed to be working concurrently in real-time. The first is the estimation of the direct illumination (incident light) from the physical scene using computer vision techniques through a 360° live-feed camera connected to AR device. The second is the simulation of indirect illumination (reflected light) from the real-world surfaces to virtual objects rendering using region capture of 2D texture from the AR camera view. The third is defining the virtual objects with proper lighting and shadowing characteristics using shader language through multiple passes. Finally, we tested our work with multiple lighting conditions to evaluate the accuracy of results based on the shadow falling from the virtual objects which should be consistent with the shadow falling from the real objects with a reduced performance cost

Finite time interaction quench in a Luttinger model

We analyze the dynamics of a Luttinger model following a quench in the electron-electron interaction strength, where the change in the interaction strength occurs over a finite time scale $\tau$. We study the Loschmidt echo (the overlap between the initial and final state) as a function of time, both numerically and within a perturbation scheme, treating the change in the interaction as a small parameter, for all $\tau$. We derive the corrections appearing in, a.) the Loschmidt echo for a finite quench duration $\tau$, b.) the scaling of the echo following a sudden ($\tau \to 0$) quench, and c.) the scaling of the echo after an adiabatic ($\tau \to \infty$) quench. We study in detail, the limiting cases of the echo in the early time and infinite time limit, and provide scaling arguments to understand these in a general context. We also show that our perturbative results are in good agreement with the exact numerical ones.Comment: 8 pages, 4 figures; updated version; to appear in Phys. Rev.

Multi-Time Schr\"odinger Equations Cannot Contain Interaction Potentials

Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schr\"odinger equations, one for each time variable. These Schr\"odinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schr\"odinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently, as we show elsewhere [17]. We also prove the following result: When a cut-off length $\delta>0$ is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schr\"odinger equations with interaction potentials of range $\delta$ are consistent; however, in the desired limit $\delta\to 0$ of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.Comment: 46 pages, 6 figures, LaTex; v2: introduction expande