Mallingspencer5045

To verify the result of the asymptotic analysis, we simulate two benchmark problems in which the body force is changed in space and time a generalized Taylor-Green problem and a natural convection problem. As a result, we find that the calculated results of macroscopic variables by the He forcing converge to those by the Guo forcing at the second-order convergence rate. Therefore, we can conclude that the He forcing and the Guo forcing are equivalent within the second-order accuracy even for the space- and time-dependent body force.We investigate a possible relation between frustration and phase-transition points in two-dimensional spin glasses at zero temperature. The relation consists of a condition on the average number of frustrated plaquettes and was reported to provide very good predictions for the critical points at zero temperature, for several two-dimensional lattices. Although there has been no proof of the relation, the good correspondence in several lattices suggests the validity of the relation and an important role of frustration in the phase transitions. To examine the relation further, we present a natural extension of the relation to diluted lattices and verify its effectiveness for bond-diluted square lattices. We then confirm that the resulting points are in good agreement with the phase-transition points in a wide range of dilution rate. Our result supports the suggestion from R. Miyazaki [J. Phys. read more Soc. Jpn. 82, 094001 (2013)JUPSAU0031-901510.7566/JPSJ.82.094001] for nondiluted lattices on the importance of frustration to the phase transition of two-dimensional spin glasses at zero temperature.We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions.Cell division is central for embryonic development, tissue morphogenesis, and tumor growth. Experiments have evidenced that mitotic cell division is manipulated by the intercellular cues such as cell-cell junctions. However, it still remains unclear how these cortical-associated cues mechanically affect the mitotic spindle machinery, which determines the position and orientation of the cell division. In this paper, a mesoscopic dynamic cell division model is established to explore the integrated regulations of cortical polarity, microtubule pulling forces, cell deformability, and internal osmotic pressure. We show that the distributed pulling forces of astral microtubules play a key role in encoding the instructive cortical cues to orient and position the spindle of a dividing cell. The present model can not only predict the spindle orientation and position, but also capture the morphological evolution of cell rounding. The theoretical results agree well with relevant experiments both qualitatively and quantitatively. This work sheds light on the mechanical linkage between cell cortex and mitotic spindle, and holds potential in regulating cell division and sculpting tissue morphology.Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbors to each point of a data set to perform their tasks. These proximity relations define a so-called geometric graph, where two nodes are linked if they are sufficiently close to each other. Random geometric graphs, where the positions of nodes are randomly generated in a subset of R^d, offer a null model to study typical properties of data sets and of machine learning algorithms. Up to now, most of the literature focused on the characterization of low-dimensional random geometric graphs whereas typical data sets of interest in machine learning live in high-dimensional spaces (d≫10^2). In this work, we consider the infinite dimensions limit of hard and soft random geometric graphs and we show how to compute the average number of subgraphs of given finite size k, e.g., the average number of k cliques. This analysis highlights that local observables display different behaviors depending on the chosen ensemble soft random geometric graphs with continuous activation functions converge to the naive infinite-dimensional limit provided by Erdös-Rényi graphs, whereas hard random geometric graphs can show systematic deviations from it. We present numerical evidence that our analytical results, exact in infinite dimensions, provide a good approximation also for dimension d≳10.The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.Previous experimental and theoretical evidence has shown that convective flow may appear in granular fluids if subjected to a thermal gradient and gravity (Rayleigh-Bénard-type convection). In contrast to this, we present here evidence of gravity-free thermal convection in a granular gas, with no presence of external thermal gradients either. Convection is here maintained steady by internal gradients due to dissipation and thermal sources at the same temperature. The granular gas is composed by identical disks and is enclosed in a rectangular region. Our results are obtained by means of an event-driven algorithm for inelastic hard disks.We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We demonstrate how schemes based on the move of single nodes between groups systematically fail at correctly sampling from the posterior distribution even on small networks, and how our merge-split approach behaves significantly better, and improves the mixing time of the Markov chain by several orders of magnitude in typical cases. We also show how the scheme can be straightforwardly extended to nested versions of the SBM, yielding asymptotically exact samples of hierarchical network partitions.We examine the underlying fracture mechanics of the human skin dermal-epidermal layer's microinterlocks using a physics-based cohesive zone finite-element model. Using microfabrication techniques, we fabricated highly dense arrays of spherical microstructures of radius ≈50μm without and with undercuts, which occur in an open spherical cavity whose centroid lies below the microstructure surface to create microinterlocks in polydimethylsiloxane layers. From experimental peel tests, we find that the maximum density microinterlocks without and with undercuts enable the respective ≈4-fold and ≈5-fold increase in adhesion strength as compared to the plain layers. Critical visualization of the single microinterlock fracture from the cohesive zone model reveals a contact interaction-based phenomena where the primary propagating crack is arrested and the secondary crack is initiated in the microinterlocked area. Strain energy energetics confirmed significantly lower strain energy dissipation for the microinterlock with the undercut as compared to its nonundercut counterpart. These phenomena are completely absent in a plain interface fracture where the fracture propagates catastrophically without any arrests. These events confirm the difference in the experimental results corroborated by the Cook-Gordon mechanism. The findings from the cohesive zone simulation provide deeper insights into soft microinterlock fracture mechanics that could prominently help in the rational designing of sutureless skin grafts and electronic skin.In this work, in the first instance, the multipseudopotential interaction (MPI) model's capabilities are extended for hydrodynamic simulations. This is achieved by combining MPI with the multiple-relaxation-time collision operator and with surface tension modification methods. A method of approaching thermodynamic consistency is also proposed, which consists of splitting the ɛ_j term into separate terms. One of these terms is used in the calculation of the interparticle force, and the second one is used in the forcing scheme. Secondly, MPI is combined with thermal models in order to simulate droplet evaporation and bubble nucleation in pool boiling. Thermal coupling is implemented using a double distribution function thermal model and a hybrid thermal model. It is found that MPI thermal models obey the D^2-law closely for droplet evaporation. MPI is also found to correctly simulate bubble nucleation and departure from the heating element during nucleate pool boiling. It can be suggested that MPI thermal models are comparatively better suited to thermal simulations at low reduced temperatures than single pseudopotential interaction models, although such cases remain very challenging. Droplet evaporation simulations are carried out at a reduced temperature (T_r) of 0.6 by setting the parameters in the Peng-Robinson equation of state to a=1/6272 and b=1/168.Epidemic spreading in heterogeneous networks has attracted great interest in recent years. To capture the significant effect of residence of individuals on epidemic spreading, we consider herein a simple susceptible-infected-susceptible model with random waiting time in heterogeneous networks. We provide the analytical dynamical expressions for the time evolution for infected individuals and find a fractional memory effect of power-law waiting time on anomalous epidemic spreading. This work provides new quantitative insights in describing contagion processes and could help model other spreading phenomena in social and technological networks.