Kinetic induced phase transition

An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is completely eliminated and only an external field is taken into account the system offers a phase transition at a finite value of the applied field. The transition is realized due to a competition between the activation processes driven by the field and the dynamical rules for the spin-flips. The result is based on a master equation approach in a quantum formulation.Comment: 13 page

Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter $p$. At a critical value $p_c^{(1)}=1/2$ where memory effects vanish there is a transition from a weakly localized regime (where the walker returns to its starting point) to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant $k = (2p-1)/t$. The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.Comment: 10 page

Competing Glauber and Kawasaki Dynamics

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability $p$ is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.Comment: 9 pages, Revte

On the Glauber model in a quantum representation

The Glauber model is reconsidered based on a quantum formulation of the Master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a single flip-process $w_i(\sigma_i)$ which is in accordance with the principle of detailed balance. The transition rate differs significantly from the conventional one due to Glauber in the low temperature regime. Here the behavior is controlled by the Ising energy and not by the microscopic time scale.Comment: 8 page

Ceramic Hollow Fiber Membranes As New Filter Media And Their Application In Oil/Water Separation Processes

Citation: Steffen Schütz, Frank Ehlen, Ina Unger, Sreenath Kariveti, Can Wang, Mehrdad Ebrahimi, Steffen Kerker, Peter Czermak: CERAMIC HOLLOW FIBER MEMBRANES AS NEW FILTER MEDIA AND THEIR APPLICATION IN OIL/WATER SEPARATION PROCESSES, in Proceedings FILTECH 2015, 24-25. February 2015, CologneCeramic membranes become continuously attractive for separation applications with fluids at increased temperatures, at high or low pH levels and in contact with critical chemical species as solvents or other organic components when polymeric membranes often fail due to high fouling or material instability. A ceramic hollow fiber membrane was developed at MANN+HUMMEL, see Figure 1. This ceramic hollow fiber membrane shows the advantages of a high volumetric filtration area and low material volumes compared to ceramic membranes with other geometries. The specific design of this membrane comprises a microfiltration ceramic support layer and an ultrafiltration ceramic functional separation layer with a pore size d90 = 40 nm. This two layer structure leads to high membrane fluxes and low pressure drop during operation. The membrane operation in cross flow mode allows the control of fouling layers due to the applied cross flow velocity. Figure 1: Cross-section of a ceramic hollow fiber membrane (MANN+HUMMEL). The operation behavior of this ceramic hollow fiber membrane was investigated for oil/water separation applications in close cooperation with a research partner and in application tests with customers. It was shown that the membrane can be operated with high oil loads up to 5000 ppm in the waste water without requiring a pretreatment. The oil contents in the permeate water were reduced to 1 ppm. Pure mechanical backflushing with permeate water was sufficient to clean the membrane in place and to reach nearly the initial flux values of the new membrane during operation. The robustness of the membrane operation in industrial applications was shown by running the membranes for several weeks in water treatment processes with industrial waste water. The waste water treatment was also promising when additional high solid loads contaminated oily waste water to be cleaned

Compensating for low topic interest and long surveys: a field experiment on nonresponse in web surveys

Certain survey characteristics proven to affect response rates, such as a survey’s length and topic, are often under limited control of the researcher. Therefore, survey researchers sometimes seek to compensate for such undesired effects on response rates by employing countermeasures such as material or nonmaterial incentives. The scarce evidence on those factors’ effects in web survey contexts is far from being conclusive. This study is aimed at filling this gap by examining the effects of four factors along with selected interactions presumed to affect response rates in web surveys. Requests to complete a web-based, selfadministered survey were sent to 2,152 owners of personal websites. The 2 X 2 X 2 X 2 fully crossed factorial design encompassed the experimental conditions of (a) high versus low topic salience, (b) short versus long survey, (c) lottery incentive versus no incentive, and (d) no feedback and general feedback (study results) versus personal feedback (individual profile of results). As expected, highly salient and shorter surveys yielded considerably higher unit-response rates. Moreover, partial support was found for interaction hypotheses derived from the leverage-salience theory of survey participation. Offering personalized feedback compensated for the negative effects of low topic salience on response rates. Also, the lottery incentive tended to evoke more responses only if the survey was short (versus long), but this interaction effect was only marginally significant. The results stress the usefulness of a multifactorial approach encompassing interaction effects to understand participation differences in web surveys. (auhtor'S abstract

Spin facilitated Ising model with long range interaction

We study the dynamics of a spin facilitated Ising model with long range kinetic constraints. To formulate those restrictions within an analytical approach we introduce the size of a kinetic active environment of a given spin. Based on a Master equation in second quantized form, the spin-autocorrelation function is calculated. It exhibits a pronounced slow dynamics, manifested by a logarithmic decay law of the spin-autocorrelation function. In case of an infinite kinetic interaction the mean field solution yields an asymptotic exact expression for the autocorrelation function which is in excellent agreement with Monte Carlo Simulations for finite interaction lengths. With increasing size of the active zone the cooperative processes, characterizing the facilitated model with short range kinetic interaction, become irrelevant. We demonstrate that the long range kinetic interaction dominates the actual spin configurations of the whole system and the mean field solution is the exact one.Comment: 18 pages, 5 figure

Reaction-controlled diffusion

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of different type B are present in their environment. Species B is subject to diffusion-limited reactions. If the density of B particles attains a finite asymptotic value (active state), the A species displays normal diffusion. On the other hand, if the B density decays algebraically ~t^{-a} at long times (inactive state), the effective attractive A-B interaction is weakened. The combination of B decay and activated A hopping processes gives rise to anomalous diffusion, with mean-square displacement ~ t^{1-a} for a < 1. Such algebraic subdiffusive behavior ensues for n-th order B annihilation reactions (n B -> 0) with n >=3, and n = 2 for d < 2. The mean-square displacement of the A particles grows only logarithmically with time in the case of B pair annihilation (n = 2) and d >= 2 dimensions. For radioactive B decay (n = 1), the A particles remain localized. If the A particles may hop spontaneously as well, or if additional random forces are present, the A-B coupling becomes irrelevant, and conventional diffusion is recovered in the long-time limit.Comment: 7 pages, revtex, no figures; latest revised versio

In situ visualization of flow and fouling layer formation in ceramic hollow fiber membranes by magnetic resonance imaging (MRI)

Within membrane processes, fouling is one of the critical issues affecting the productivity, plant operation and maintenance costs. Focusing on wastewater treatment processes, it has been reported that extracellular polymeric substances (EPS) are one of the main causes of membrane fouling. In membrane filtration research, sodium alginate often serves as a model compound for EPS. Sodium alginate is a hydrophilic unbranched binary copolymer. In the presence of divalent cations, e.g. Ca2+, alginates form complexes, which lead to a significant change in filtration mechanisms in dead-end filtration and also to a change in filtration performance during cross-flow filtration experiments. Filtration conditions (e.g. transmembrane pressure or cross flow velocity), feed composition as well as membrane material have a major influence on the fouling behavior of the system. In this study ceramic hollow fiber membranes were used due to their high chemical and thermal stability coupled with a high specific membrane surface. In addition to the evaluation of the filtration data using conventional cake filtration model, nuclear magnetic resonance imaging was used to elucidate the influence of Ca2+ on the fouling layer structure for alginate filtration with ceramic hollow fiber membranes. In order to visualize the alginate layers inside the opaque ceramic hollow fiber membranes by means of MRI, specific contrast agents were applied. Supplementary to multi slice multi echo imaging, flow velocity measurements were performed to gain more insight into the hydrodynamics in the fouled membranes. MRI reveals the structure of the alginate layers and confirms the assumption obtained from the evaluation of filtration data, that the addition of Ca2+ is leading to the formation of an alginate gel layer on the membrane, whereas in the absence of Ca2+, the structure of the alginate layer is rather of concentration polarization manner, hence more fluid and hydrodynamically better controllable