A numerical method for computing three-dimensional Stokes flow driven by a doubly-periodic array of regularized forces is presented. In the non-periodic direction either a free boundary or a homogeneous Dirichlet condition is enforced. The method consists of finding a regularized Green's function in Fourier space analytically. Then only an inverse fast Fourier transform (inverse FFT) has to be computed. Accuracy is verified by comparing numerical results to a solution that is independent of the method. In an Ewald splitting, the FFT method can be used to compute the smooth component of the flow, which allows for a splitting parameter as small as a few grid cells. This selection makes the sum in physical space converge extremely fast. Numerical examples demonstrate that fact. Since the forces are regularized, in some cases splitting is not even needed, depending on the relative sizes of the numerical parameters. The method is applied to model the flow created by carpets of nodal cilia based on cilium shape. / acase@tulane.edu

No / Baltic Germans who were active on behalf of especially German minorities throughout Europe during the 1920s have already found some recognition in especially German-language studies. Now they are receiving a wider coverage. Two of these men, Werner Hasselblatt and Ewald Ammende, came from Estonia and played a part in the development of the cultural autonomy legislation enacted in 1925. Traditionally this has been counted a positive contribution to the management of Europe's minorities during the inter-war period. During the 1930s at the latest, however, both Hasselblatt and Ammende drifted towards German National Socialism. Through an investigation of the ideas of these men, this paper attempts to interpret lives which helped to create apparently progressive legislation in the 1920s, but which compromised with a dreadful political movement soon afterwards. What were the motives behind their actions?

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

Den Schwerpunkt der zweisprachig (deutsch-litauisch) geschriebenen Abhandlung bilden Aussagen zur Freundschaft und zum Umgang der Brüder Grotthuß mit C. Ph. E. Bach. Melnikas wertet dabei die mehrfach den Namen Grotthuß aufweisenden Bachschen Pränumerantenlisten ebenso aus, wie er auf D. E. von Grotthuß\'' Kollekteurstätigkeit in diesem Zusammenhang eingeht.

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.

One of the most important aspects for all life on this planet is the act to keep their biological processes in a state where they do not reach equilibrium. One part in the upholding of this imbalanced state is the barrier between the cells and their surroundings, created by the cell membrane. Additionally, terrestrial animal life often requires a barrier that protects the organism's body from external hazards and water loss. As an alternative to experiments, the investigation of the processes occurring at these barriers can be performed by using molecular dynamics simulations. Through this method we can obtain an atomistic description of the dynamics associated with events that are not accessible to experimental setups.  In this thesis the first paper presents an improved particle-mesh Ewald method for the calculation of long-range Lennard-Jones interactions in molecular dynamics simulations, which solves the historical performance problem of the method. The second paper demonstrate an improved implementation, with a higher accuracy, that only incurs a performance loss of roughly 15% compared to conventional simulations using the Gromacs simulation package. Furthermore, the third paper presents a study of cholesterol's effect on the permeation of six different solutes across a variety of lipid bilayers. A laterally inhomogeneous permeability in cholesterol-containing membranes is proposed as an explanation for the large differences between experimental permeabilities and calculated partition coefficients in simulations. The fourth paper contains a coarse-grained simulation study of a proposed structural transformation in ceramide bilayer structures, during the formation of the stratum corneum. The simulations show that glycosylceramides are able to stabilize a three-dimensionally folded bilayer structure, while simulations with ceramides collapse into a lamellar bilayer structure. / <p>QC 20160308</p>

Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green&rsquo / s function in layered media which is expressed as an infinite series in terms of the spectral domain Green&rsquo / s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green&rsquo / s function. First, the spectral domain Green&rsquo / s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald&rsquo / s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green&rsquo / s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.

One of the most important aspects for all life on this planet is theact to keep their cellular processes in a state where they do notreach equilibrium. One part in the upholding of this imbalanced stateis the barrier between the cells and their surroundings, created bythe cell membrane. In addition to experiments, the investigation ofprocesses occuring in the cell membrane can be performed by usingmolecular dynamics simulations. Through this method we can obtain anatomistic description of the dynamics associated with events that arenot accessible to experimental setups. Molecular dynamics relies onthe integration of Newton's equations of motion in order to sample therelevant parts of phase-space for the system, and therefore it isdependent on a correct description of the interactions between all thesimulated particles. In this thesis I first present an improved methodfor the calculation of long-range interactions in molecular dynamicssimulations, followed by a study of cholesterol's impact on thepermeation of small solutes across a lipid bilayer. The first paper presents a previously derived modification to theparticle-mesh Ewald method, which makes it possible to apply thisto long-range Lennard-Jones interactions. Old implementations of themethod have been haunted by an extreme performance degradation andhere I propose a solution to this problem by applying a modifiedinteraction potential. I further show that the historical treatmentof long-range interactions in simulations of lipid bilayers hasnon-negligible effects on their structural properties.In the second paper, this modification is improved such that the smallerrors introduced by the modified interaction potential becomenegligible. Furthermore, I demonstrate that I have also improved theimplementation of the method so that it now only incurs a performanceloss of roughly 15% compared to conventional simulations using theGromacs simulation package.The third paper presents a simulation study of cholesterol's effect onthe permeation of six different solutes across a variety of lipidbilayers. I analyze the effect of different head groups, tail lengths,and tail saturation by performing simulations of the solutes in fourdifferent bilayers, with cholesterol contents between 0% and50%. Analysis of the simulations shows that the impact of the surfacearea per lipid on the partitioning of the solute could be lower thanpreviously thought. Furthermore, a model with a laterallyinhomogeneous permeability in cholesterol-containing membranes isproposed, which could explain the large differences betweenpermeabilities from experiments and calculated partition coefficientsin simulations. / <p>QC 20140609</p>

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