Three-dimensional (3D) computational modeling and simulation are presented on the motion of a large number of deformable cells in microchannels. The methodology is based on an immersed boundary method, and the cells are modeled as liquid-filled elastic capsules. The model retains two important features of the blood flow in the microcirculation, that is, the particulate nature of blood and deformation of the erythrocytes. The tank-treading and tumbling motion and the lateral migration, as observed for erythrocytes in dilute suspension, are briefly discussed. We then present results on the motion of multiple cells in semidense suspension and study how their collective dynamics leads to various physiologically relevant processes such as the development of the cell-free layer and the Fahraeus-Lindqvist effect. We analyze the 3D trajectory and velocity fluctuations of individual cell in the suspension and the plug-flow velocity profile as functions of the cell deformability, hematocrit, and vessel size. The numerical results allow us to directly obtain various microrheological data, such as the width of the cell-free layer, and the variation in the apparent blood viscosity and hematocrit over the vessel cross section. We then use these results to calculate the core and plasma-layer viscosity and show that the two-phase (or core-annular) model of blood flow in microvessels underpredicts the blood velocity obtained in the simulations by as much as 40%. Based on a posteriori analysis of the simulation data, we develop a three-layer model of blood flow by taking into consideration the smooth variation in viscosity and hematocrit across the interface of the cell-free layer and the core. We then show that the blood velocity predicted by the three-layer model agrees very well with that obtained from the simulations.

The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose an alternative point of view, making use of concepts taken from the field of computational geometry, where the definition of the “shape” of a set of points is a well-known problem. In particular, we employ the $\alpha$-shape construction which, applied to the positions of the molecules, selects a shape and identifies its boundary points, which we will take to define our interfacial molecules. A single parameter needs to be fixed (the “$\alpha$” of the $\alpha$ shape), and several proposals are examined, all leading to very similar choices. Results of this methodology are evaluated against previous proposals, and seen to be reasonable.

The initial motion of two-dimensional capsule in microchannel flow just after release is investigated in this paper by a numerical simulation method, which combines the finite volume method with the front tracking technique. The capsule is modeled as liquid medium enclosed by a thin membrane, for which linear elastic properties are taken into consideration. Three kinds of initial capsule shapes (circle, ellipse, and biconcave) and three initial positions (center-line, near-center, and near-wall positions) are considered in the simulations. Off-center capsules (the near-center and near-wall capsules) experience tilting and membrane tank-treading, and migrate laterally while they move with the fluid flow. After initial rapid tilting, the circular and elliptic near-wall capsules reach quasistationary tilt orientation, while the biconcave near-wall capsules experience steady change in tilt orientation with time. Lateral movements of the capsules indicate the existence of lift effect causing the capsule to move away from the wall. Lift velocities, the velocity components along the transverse direction, of the circular near-wall capsules decrease as they approach the centerline, while those of the elliptic and biconcave near-wall capsules do not show this trend, which might result from the short range of the simulation time. In general, the capsule with higher membrane dilation modulus has lower lift velocity, showing the effect of capsule deformability on the capsule behavior. Both tank-treading and lift velocities are 1–2 orders lower than the capsule translational velocity. For the circular and biconcave capsules, no matter the center-line or off-center capsules, hematocrit ratio increases with the membrane dilation modulus, namely, the capsule moving velocity decreases with the increasing dilation modulus, while the elliptic capsules with nondimensional membrane dilation moduli of 2500 and 500 show inverse trend in some time range. A preliminary study is carried out for long-term simulation of a circular capsule.

This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.

We study a classical fully frustrated honeycomb lattice Ising model using Markov-chain Monte Carlo methods and exact calculations. The Hamiltonian realizes a degenerate ground-state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins $N$. Traditional single-spin-flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a nonlocal “chain-flip” algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond and an external magnetic field $h$. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with nonextensive entropy are found, and two special values of $h$ exist where the residual entropy again becomes extensive, scaling proportionally to $N\text{ln}\varphi$, where $\varphi$ is the golden ratio.

We study the transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion, and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean-square displacement. However, quasidiffusion is an anomalous transport regime. We established that a change in transport regimes in time leads to a change in regimes in space. Concentration tails have a cascade structure, namely, consisting of several parts.

We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.

A theoretical formulation and corresponding numerical solutions are presented for fluid flow and sediment transport past evolutionary sand dunes. Time-dependent curvilinear coordinates are employed to fully couple flow aloft with the developing landform. The differential conservation law that defines shape of the lower boundary depends on details of local surface stress, thereby favoring the large eddy simulation of the boundary layer. To shrink the gap between the time scales characteristic of planetary boundary layer flows $O\left({10}^3\right)\text{s}$ and sand dune evolution $O\left({10}^6\right)\text{s}$, a hypothetical “severe-wind scenario” is adopted with the saltation flux amplified up to 3 orders of magnitude. While the results are largely insensitive to the rescaling, the efficacy of computations is greatly improved. The flux-form partial differential equation for the interface profile—via saltation and sand avalanches—is formulated as an advection-diffusion equation, to facilitate discrete integrations. Numerical experiments verify the adopted theoretical framework by reproducing scaling results reported in the literature. The versatility of the approach is illustrated with evolution of a sandhole—an example of application likely never addressed in the literature, yet realizable in nature.

A fundamental difference between fluids and solids is their response to applied shear. Solids possess static shear moduli, while fluids do not. Complex fluids such as foams display an intermediate response to shear with nontrivial frequency-dependent shear moduli. In this paper, we conduct coordinated experiments and numerical simulations of model foams subjected to boundary-driven oscillatory planar shear. Our studies are performed on bubble rafts (experiments) and the bubble model (simulations) in two dimensions. We focus on the low-amplitude flow regime in which T1 events, i.e., bubble rearrangement events where originally touching bubbles switch nearest neighbors, do not occur, yet the system transitions from solid- to liquidlike behavior as the driving frequency is increased. In both simulations and experiments, we observe two distinct flow regimes. At low frequencies $\omega$, the velocity profile of the bubbles increases linearly with distance from the stationary wall, and there is a nonzero total phase shift between the moving boundary and interior bubbles. In this frequency regime, the total phase shift scales as a power law $\Delta \sim {\omega }^n$ with $n\approx 3$. In contrast, for frequencies above a crossover frequency $\omega >{\omega }_p$, the total phase shift $\Delta$ scales linearly with the driving frequency. At even higher frequencies above a characteristic frequency ${\omega }_{nl}>{\omega }_p$, the velocity profile changes from linear to nonlinear. We fully characterize this transition from solid- to liquidlike flow behavior in both the simulations and experiments and find qualitative and quantitative agreements for the characteristic frequencies.

We present a theoretical study of adhesion-induced lateral phase separation for a membrane with short stickers, long stickers, and repellers confined between two hard walls. The effects of confinement and repellers on lateral phase separation are investigated. We find that the critical potential depth of the stickers for lateral phase separation increases as the distance between the hard walls decreases. This suggests confinement-induced or force-induced mixing of stickers. We also find that repellers with stronger repulsive potential tend to enhance, while repellers with weaker repulsive potential tend to suppress adhesion-induced lateral phase separation.

In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its three-dimensional (3D) counterpart by having a second quadratic conserved variable in addition to the energy and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity $V$ and energy $K$ as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with $K$ in wall units increasing logarithmically with the Reynolds number ${\text{Re}}_{\tau }$ instead of being ${\text{Re}}_{\tau }$ independent in 3D channels.

Hydrodynamic interactions between two semiflexible inextensible filaments are shown to have a significant impact on filament buckling and their subsequent motion in Stokesian fluids. In linear shear flow, hydrodynamic interactions lead to filament shear dispersion that depends on the filament aspect ratio and the initial filament separation. In linear extensional flow, hydrodynamic interactions lead to complex filament dynamics around the stagnation point. These results suggest that hydrodynamic interactions need to be taken into account to determine the self-diffusion of non-Brownian semiflexible filaments in a cellular flow [Y.-N. Young and M. J. Shelley, Phys. Rev. Lett. 99, 058303 (2007)].

Solitary waves in continuum media pass through each other with only a slight phase change. However, in an intrinsically nonlinear many-body system such solitary waves could behave differently. It was predicted and experimentally confirmed that head-on solitary wave collisions in granular alignments are followed by the formation of tiny secondary solitary waves in the vicinity of the collision point. While it remains a challenge to provide an analytical treatment of the local time evolution, we present arguments and associated simulations to address a crucial unknown, namely, why the secondary solitary waves must form. Extensive numerical investigations on solitary wave collisions at a grain center and at an edge show marked differences. The effects of softening the grain repulsion are discussed to validate the arguments.

A lattice Boltzmann equation (LBE) for axisymmetric flows is proposed. The model has some distinct features that distinguish it from existing axisymmetric LBE models. First, it is derived from the Boltzmann equation so that it has a solid physics base and is easy for generalization; second, the model can describe the axial, radial, and azimuthal velocity components in the same fashion; and third, the source terms of the model contain no velocity gradients and are much simpler than other LBE models. Numerical tests, including steady and unsteady internal and external flows, demonstrate that the proposed LBE can serve as a viable and efficient method for low speed axisymmetric flows.

This investigation employs a hierarchical lattice and renormalization-group methodology to probe the effects of competing crystal-field interactions in a Blume-Capel Ising system. Several phase diagrams have been produced in temperature–crystal-field space as the strength of the competing crosslink crystal-field interactions is varied. Each sink has been interpreted and critical exponents have been calculated for the higher-order transitions.

We present systematic investigations of buckling in Langmuir monolayers of polyvinyl acetate formed at the air-water interface. On compression the polymer monolayers are converted to a continuous membrane with a thickness of $\sim 2–3\text{nm}$ of well-defined periodicity, ${\lambda }_b$. Above a certain surface concentration the membrane undergoes a morphological transition buckling, leading to the formation of striped patterns. The periodicity seems to depend on molecular weight as per the predictions of the gravity-bending buckling formalism of Milner et al. for fluidlike films on water. However anomalously low values of bending rigidity and Young’s modulus are obtained using this formalism. Hence we have considered an alternative model of buckling-based solidlike films on viscoelastic substrates. The values of bending rigidity and Young’s modulus obtained by this method, although lower than expected, are closer to the bulk values. Remarkably, no buckling is found to occur above a certain molecular weight. We have tried to explain the observed molecular-weight dependence in terms of the variation in isothermal compressive modulus of the monolayers with surface concentration as well as provided possible explanations for the obtained low values of mechanical properties similar to that observed for ultrathin polymer films.

An elastic spring model is applied to simulate the skeletal structure of the red blood cell (RBC) membrane and to study the dynamical behaviors of the red blood cell rouleaux (aggregates) in microchannels. The biconcave shape of RBCs in static plasma and the tank-treading phenomenon of single RBCs in simple shear flows have been successfully captured using this model. The aggregation and dissociation of RBCs with different deformability have been investigated in both shear and Poiseuille flows by taking into consideration the rheology of the cells and the intercellular interaction kinetics. It is found that the equilibrium configuration of the rouleaux formed under no-flow condition, the motion of the rouleaux in the flows, and the rheological behavior of individual cells in the rouleaux is closely related to the intercellular interaction strength, hydrodynamic viscous forces, and the deformability of the cell membrane.

The country neighborhood network, where nodes represent countries and two nodes are considered linked if the corresponding countries are neighbors on territory, is created and its giant component, the Asia, Europe, and Africa (AEA) cluster, is carefully studied in this paper. It is found that, as common, the degree distribution and the clustering function of the AEA cluster are both compatible with scale-free property, besides, the AEA cluster presents a little disassortativity, and its near power-law country area-degree relationship with the exponent close to 1.7 may imply a fractal dimension close to 1.2 of country borderlines in the AEA continent. It is also revealed that the average difference of population density between two countries obeys an approximately increasing function of the shortest path length between them, which may suggest a gradual consensus of population density in the AEA cluster. A simple unity rule is then adopted to model the AEA cluster and such model explains the AEA cluster very well in most aspects, e.g., power-law domain area distribution and fractal domain borderlines, etc., except that the network derived by the model has stronger disassortativity, which may be explained by the fact that, in the evolution history of countries, unbalanced neighbors are more likely to be united as one than balanced neighbors. Additionally, the network evolving process can be divided into three periods, defined as formation period, growth period, and combination period, and there are indications that the AEA cluster is in its third period.

Lévy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining $\alpha$-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst “sizes” and “durations” in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.

We propose a nonlinear random-walk model to describe the dynamics of dense contaminant plumes in porous media. A coupling between concentration and velocity fields is found so that transport displays non-Fickian features. The qualitative behavior of the pollutant spatial profiles and moments is explored with the help of Monte Carlo simulation, within a continuous-time random-walk approach. Model outcomes are then compared with experimental measurements of variable-density contaminant transport in homogeneous and saturated vertical columns.