A Path Intergal Approach to Current

Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schr\"odinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a uni-directional current at the boundary of the support. We use path integrals to define current and uni-directional current and give a direct derivation of the expression for current from the path integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short time propagation of initial wave function with compact support for both the cases of discontinuous derivative and discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O(\Delta t)$. This gives a decay law.Comment: 17 pages, Late

Monitored data on occupants’ presence and actions in an office building

Within a study, an open plan area and one closed office in a university building with a floor area of around 200 m2 were monitored. The present data set covers a period of one year (from 2013-01-01 to 2013-12-31). The collected data pertains to indoor environmental conditions (temperature, humidity) as well as plug loads and external factors (temperature, humidity, wind speed, and global irradiance) along with occupants’ presence and operation of windows and lights. The monitored data can be used for multiple purposes, including the development and validation of occupancy-related models

Kultur im Deutsch als Fremdsprache-Unterricht

Abstract . In dieser Kandidatenarbeit wird die Rolle von Kultur im Deutsch als Fremdsprache-Unterricht analysiert. Das Hauptaugenmerk liegt hierbei auf Lehrbüchern mit ihren verschiedenen Texten und Übungen. Laut dem finnischen Lehrplan spielen Kultur und Kulturaspekte eine wichtige Rolle im Fremdsprachenunterricht. Vorurteile sollen abgebaut werden und die Schüler sollen auf den Umgang mit anderen Kulturen vorbereitet werden. Aus diesem Grund vergleicht diese Arbeit die vorhandenen Inhalte der Lehrbücher mit den Richtlinien des finnischen Lehrplans. Die Lehrbücher mit ihren Bildern sind es auch, die Schülern einen Einblick in die Kultur und Lebensweise der Menschen gibt, die Deutsch als Muttersprache sprechen. Hierbei ist zu erwähnen, dass sich die Gesellschaft und verschiedene vorhandene Kulturen auf Grund von Migration verändert haben. Diese Veränderung sollte auch in den Bildern der Lehrbücher zu finden sein. Anhand einer qualitativen Inhaltsanalyse wird in dieser Arbeit jedoch gezeigt, dass sich die Gesellschaft schneller verändert als der Inhalt der Lehrbücher. Deshalb wird mit Hilfe von künstlicher Intelligenz versucht, bessere Bilder für Lehrbücher zu erstellen. Verschiedene Kulturkonzepte wie das Behälterkonzept, Stereotype und interkulturelle Kommunikation werden dabei berücksichtigt. Auch die künstliche Intelligenz braucht spezielle Anleitungen, sodass Stereotype vermieden werden. Zusätzlich wird versucht, Aspekte wie Gemeinsamkeit und Offenheit in möglichen Bildern für Lehrbücher darzustellen. Wenn Bilder für Texte und Aufgaben in Lehrbüchern aus bestehenden Datenbanken verwendet werden, kann es sein, dass Schüler ein falsches oder veraltetes Bild über die Gesellschaft in deutschsprachigen Ländern erhalten. Deshalb ist es wichtig, dass verschiedene Kulturhintergründe durch Migration, die es heutzutage in der Gesellschaft gibt, in den Bildern wiederzuerkennen sind. Als Ergebnis dieser Arbeit werden verschiedene Beispiele für Bilder gezeigt, die es ermöglichen, die vorhandenen Aufgabenstellungen in Lehrbüchern zu verbessern

Brownian Simulations and Uni-Directional Flux in Diffusion

Brownian dynamics simulations require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages. The continuum baths are connected to the simulation through interfaces, located in the baths sufficiently far from the channel. Average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the interfaces. The particles injected into the simulation volume represent a unidirectional diffusion flux, while the outgoing particles represent the unidirectional flux in the opposite direction. The classical diffusion equation defines net diffusion flux, but not unidirectional fluxes. The stochastic formulation of classical diffusion in terms of the Wiener process leads to a Wiener path integral, which can split the net flux into unidirectional fluxes. These unidirectional fluxes are infinite, though the net flux is finite and agrees with classical theory. We find that the infinite unidirectional flux is an artifact caused by replacing the Langevin dynamics with its Smoluchowski approximation, which is classical diffusion. The Smoluchowski approximation fails on time scales shorter than the relaxation time $1/\gamma$ of the Langevin equation. We find the unidirectional flux (source strength) needed to maintain average boundary concentrations in a manner consistent with the physics of Brownian particles. This unidirectional flux is proportional to the concentration and inversely proportional to $\sqrt{\Delta t}$ to leading order. We develop a BD simulation that maintains fixed average boundary concentrations in a manner consistent with the actual physics of the interface and without creating spurious boundary layers

Maximum Path Information and Fokker-Planck Equation

We present in this paper a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy) and the time t.Comment: 7 page

Thermophoresis of Brownian particles driven by coloured noise

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory. The noise characteristic time scale is typically of the same order as the time over which the particle's kinetic energy is lost due to friction (inertial time scale). We demonstrate theoretically that, in the presence of a temperature gradient, the interplay between these two characteristic time scales can have measurable consequences on the particle long-time behaviour. Using homogenization theory, we analyse the infinitesimal generator of the stochastic differential equation describing the system in the limit where the two characteristic times are taken to zero; from this generator, we derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Furthermore, studying the long-term stationary particle distribution, we show that particles can accumulate towards the colder (positive thermophoresis) or the warmer (negative thermophoresis) regions depending on the dependence of their physical parameters and, in particular, their mobility on the temperature.Comment: 9 pages, 4 figure

Robust synchronization of a class of coupled delayed networks with multiple stochastic disturbances: The continuous-time case

In this paper, the robust synchronization problem is investigated for a new class of continuous-time complex networks that involve parameter uncertainties, time-varying delays, constant and delayed couplings, as well as multiple stochastic disturbances. The norm-bounded uncertainties exist in all the network parameters after decoupling, and the stochastic disturbances are assumed to be Brownian motions that act on the constant coupling term, the delayed coupling term as well as the overall network dynamics. Such multiple stochastic disturbances could reflect more realistic dynamical behaviors of the coupled complex network presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques and the properties of Kronecker product, we derive several delay-dependent sufficient conditions that ensure the coupled complex network to be globally robustly synchronized in the mean square for all admissible parameter uncertainties. The criteria obtained in this paper are in the form of linear matrix inequalities (LMIs) whose solution can be easily calculated by using the standard numerical software. The main results are shown to be general enough to cover many existing ones reported in the literature. Simulation examples are presented to demonstrate the feasibility and applicability of the proposed results

Temporal dynamics of tunneling. Hydrodynamic approach

We use the hydrodynamic representation of the Gross -Pitaevskii/Nonlinear Schroedinger equation in order to analyze the dynamics of macroscopic tunneling process. We observe a tendency to a wave breaking and shock formation during the early stages of the tunneling process. A blip in the density distribution appears in the outskirts of the barrier and under proper conditions it may transform into a bright soliton. Our approach, based on the theory of shock formation in solutions of Burgers equation, allows us to find the parameters of the ejected blip (or soliton if formed) including the velocity of its propagation. The blip in the density is formed regardless of the value and sign of the nonlinearity parameter. However a soliton may be formed only if this parameter is negative (attraction) and large enough. A criterion is proposed. An ejection of a soliton is also observed numerically. We demonstrate, theoretically and numerically, controlled formation of soliton through tunneling. The mass of the ejected soliton is controlled by the initial state.Comment: 11 pages, 6 figures, expanded and more detailed verions of the previous submissio

Diffusion Process in a Flow

We establish circumstances under which the dispersion of passive contaminants in a forced, deterministic or random, flow can be consistently interpreted as a Markovian diffusion process. In case of conservative forcing the repulsive case only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded from below, is unquestionably admitted by the compatibility conditions. A class of diffusion processes is exemplified, such that the attractive forcing is allowed as well, due to an appropriate compensation coming from the "pressure" term. The compressible Euler flows form their subclass, when regarded as stochastic processes. We establish circumstances under which the dispersion of passive contaminants in a forced, deterministic or random, flow can be consistently interpreted as a Markovian diffusion process. In case of conservative forcing the repulsive case only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded from below, is unquestionably admitted by the compatibility conditions. A class of diffusion processes is exemplified, such that the attractive forcing is allowed as well, due to an appropriate compensation coming from the "pressure" term. The compressible Euler flows form their subclass, when regarded as stochastic processes.Comment: 10 pages, Late