Imbibition of micropatterned surfaces can have broad technological and fundamental implications for areas ranging from biomedical devices and fuel transport to writing with ink. Despite rapidly growing interests aimed at various applications, a fundamental physical understanding of the imbibition dynamics is still in its infancy. Recently, two simple scaling regimes for the dynamics have been established for a textured surface decorated with long pillars whose top and bottom edges are sharp. Here, we study the imbibition dynamics of textured surfaces decorated by short pillars with rounded edges, to find a different scaling regime. Interestingly, this regime originates not from the balance of two effects but from the hybrid balance of three effects. Furthermore, this scaling law can be universal or independent of the details of the texture geometry. We envision that this potentially universal scaling regime might be ubiquitous and will be useful in the handling and transportation of a small amount of liquid.

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-$\mathit{XY}$ model. In this chain, the cluster term and the $\mathit{XY}$ couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as $p_{\downarrow }=p{p}_d$ and $p_{\uparrow }=p(1-p_d)$, with $p$ representing the average occupation probability and $p_d$ controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to $p_d=1/2$ and $p_d=0,1$ respectively. In this work, besides IP and DP, we also consider the $1/2<p_d<1$ region. Extensive Monte Carlo simulations are carried out on the square and the simple-cubic lattices, and the numerical data are analyzed by finite-size scaling. We locate the percolation thresholds of the BDP model for $p_d=0.6$ and $0.8$, and determine various critical exponents. These exponents are found to be consistent with those for standard DP. We also determine the renormalization exponent associated with the asymmetric perturbation due to $p_d-1/2\ne 0$ near IP, and confirm that such an asymmetric scaling field is relevant at IP.

By event-driven molecular dynamics simulations, we study the Leidenfrost effect for wet granular matter driven from below. In marked contrast to all earlier studies on other fluids, the dense plug hovering on the hot gas cushion undergoes an undamped oscillation. The location of the Hopf bifurcation leading to this oscillation is strongly dependent on the inelasticity of the grain impacts. The vertical separation into a gas phase with a condensed plug hovering above it is particularly pronounced due to the cohesiveness of the granulate. For sufficiently large system sizes, the Rayleigh-Taylor instability terminates the oscillatory state at late times.

We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes rays of stress to propagate away from a point force at oblique angles. Prior verifications of the null stress law have used a sequential packing method which yields packs with anisotropic packing histories. We create packs without this anisotropy, and then later break the symmetry by adding a boundary. Our isotropic packs are very sensitive, and their responses to point forces diverge wildly, indicating that they cannot be described by any continuum stress model. We stabilize the packs by supplying an additional boundary, which makes the response much more regular. The response of the stabilized packs resembles what one would expect in a hyperstatic pack, despite the isostatic bulk. The expected stress rays characteristic of null stress behavior are not present. This suggests that isostatic packs do not need to obey a null stress condition. We argue that the rays may arise instead from more simple geometric considerations, such as preferred contact angles between beads.

The interaction of two diffusing particles is strongly influenced by their hydrodynamic coupling. At a tracking rate of 10 kHz we are able to measure the 3D trajectories of two colloidal spheres in a single harmonic potential, which was generated by scanning line optical tweezers. This common potential enables tilting, rotational, and translational dynamics of the spheres, which we analyzed via the spheres position cross-correlations $C\left(\tau \right)$ over a time range of ${10}^{-4}$–2 s. We found that the dynamic interaction of the colloids is controlled by short-range surface forces ${\mathit{F}}_s$, which are attractive in one direction and repulsive in the other two directions. This unexpected behavior is supported by a theoretical model using two Langevin equations, which decouple for linear ${\mathit{F}}_s$, allowing a description with autocorrelation functions for collective and relative motions. We further demonstrate that variations in salt concentration and reaction volumes significantly influence $C\left(\tau \right)$ and the mean contact times between the particles, which may offer new insights into biological particle interaction.

Short single-stranded nucleic acids are ubiquitous in biological processes; understanding their physical properties provides insights to nucleic acid folding and dynamics. We used small-angle x-ray scattering to study 8–100 residue homopolymeric single-stranded DNAs in solution, without external forces or labeling probes. Poly-T's structural ensemble changes with increasing ionic strength in a manner consistent with a polyelectrolyte persistence length theory that accounts for molecular flexibility. For any number of residues, poly-A is consistently more elongated than poly-T, likely due to the tendency of A residues to form stronger base-stacking interactions than T residues.

Bubble damping in displacement-driven microfluidic flows was theoretically and experimentally investigated for a Y-channel microfluidic network. The system was found to exhibit linear behavior for typical microfluidic flow conditions. The bubbles induced a low-pass filter behavior with a characteristic cutoff frequency that scaled proportionally with flow rate and inversely with bubble volume and exhibited a minimum with respect to the relative resistances of the connecting channels. A theoretical model based on the electrical circuit analogy was able to predict experimentally observed damping of fluctuations with excellent agreement. Finally, a flowmeter with high resolution (0.01 μL/min) was demonstrated as an application of the bubble-aided stabilization. This study may aid in the design of many other bubble-stabilized microfluidic systems.

Based on the linear response theory and the diagram technique of the perturbation theory, the correlation between the homogeneous and isotropic Coulomb system permittivity features caused by the nonzero static conductivity and the effects of external electrostatic field screening is determined. The results obtained can be used to study the metal-dielectric transition at zero temperature beyond the scope of the adiabatic approximation for nuclei. It is shown that at the critical point the matter consisting of electrons and nuclei of the same type is in the “true” dielectric state characterized by the zero static conductivity and the absence of screening of the weak electrostatic field.

Mass conservation and momentum transfer across solid-fluid boundaries have been active topics through the development of the lattice-Boltzmann method. In this paper, we review typical treatments to prevent net mass transfer across solid-fluid boundaries in the lattice-Boltzmann method, and argue that such efforts are in general not necessary and could lead to incorrect results. Carefully designed simulations are conducted to examine the effects of normal boundary movement, tangential density gradient, and lattice grid resolution. Our simulation results show that the global mass conservation can be well satisfied even with local unbalanced mass transfer at boundary nodes, while a local mass conservation constraint can produce incorrect flow and pressure fields. These simulations suggest that local mass conservation, at either a fluid or solid boundary node, is not only an unnecessary consequence to maintain the global mass conservation, but also harmful for meaningful simulation results. In addition, the concern on the momentum addition and reduction associated with status-changing nodes is also not technically necessary. Although including this momentum addition or reduction has no direct influence on flow and pressure fields, the incorrect fluid-particle interaction may affect simulation results of particulate suspensions.

The Kramers-Moyal analysis is a well-established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process, which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.

The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general $d$-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general $d$ expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of $1/d$.

The effects of bond randomness on the universality aspects of a two-dimensional ($d=2$) Blume-Capel model embedded in the triangular lattice are discussed. The system is studied numerically in both its first- and second-order phase-transition regimes by a comprehensive finite-size scaling analysis for a particularly suitable value of the disorder strength. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the two-dimensional (2D) random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs again to the same universality class. Although the first finding reinforces the scenario of strong universality in the 2D Ising model with quenched disorder, the second is in difference from the critical behavior, emerging under randomness, in the cases of the ex-first-order transitions of the Potts model. Finally, our results verify previous renormalization-group calculations on the Blume-Capel model with disorder in the crystal-field coupling.

We present a generalized transmission coefficient formula for the lead-junction-lead system, in which interaction between the leads has been taken into account. Based on this formula, the Caroli formula could be easily recovered and a transmission coefficient formula for interface problem in the ballistic system can be obtained. The condition of validity for the formula is carefully explored. We mainly focus on heat transport. However, the corresponding electrical transport could be similarly dealt with. Also, an illustrative example is given to clarify the precise meaning of the quantities used in the formula, such as the concept of the reduced interacting matrix in different situations. In addition, an explicit transmission coefficient formula for a general one-dimensional interface setup is obtained based on the derived interface formula.

Using the phenomenological expression for the level spacing distribution with only one parameter $0\le \beta \le \infty$ covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between $\beta$ and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the parameter $\beta$ and the strength of the coupling to the continuum. For nonperfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by $\beta$ and the degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.

We consider a minimalistic dynamic model of the idiotypic network of B lymphocytes. A network node represents a population of B lymphocytes of the same specificity (idiotype), which is encoded by a bit string. The links of the network connect nodes with complementary and nearly complementary bit strings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists; otherwise it is empty. There is a continuous influx of new B lymphocytes of random idiotype from the bone marrow. B lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors; unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which make it possible to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.

We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular architectures, the building principles of which are known. The nodes of the network can be classified into groups of nodes, the modules, which share statistical properties. Each node experiences only the mean influence of the groups to which it is linked. Given the size of the groups and linking between them the statistical properties such as mean occupation, mean lifetime, and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations. For a pattern which consists of pairs of occupied nodes correlations are taken into account.

Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics of plain lipid membranes in experimental model systems are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, and the rearrangement of the lipid molecules. We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its midsurface and by a lipid density field for each monolayer. The viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the inter-monolayer friction and the membrane interfacial shear viscosity. While the bilayer equilibria are well understood theoretically, dynamical calculations have relied on simplified continuum approaches of uncertain transferability, or on molecular simulations reaching very limited length and time scales. Our approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We validate it with the well understood tether extension. We investigate the tubular lipid transport between cells, the dynamics of bud absorption by a planar membrane, and the fate of a localized lipid density asymmetry in vesicles. These axisymmetric examples bear biological relevance and highlight the diversity of dynamical regimes that bilayers can experience.

Intracellular biochemical reactions exhibit a rich dynamical phenomenology which cannot be explained within the framework of mean-field rate equations and additive noise. Here, we show that the presence of metastable states and radically different time scales are general features of a broad class of autocatalytic reaction networks, and that this fact may be exploited to gain analytical results. The latter point is demonstrated by a treatment of the paradigmatic Togashi-Kaneko reaction, which has resisted theoretical analysis for the last decade.

We add thermal noise consistently to reduced models of undeformable vesicles and capsules in shear flow and derive analytically the corresponding stochastic equations of motion. We calculate the steady-state probability distribution function and construct the corresponding phase diagrams for the different dynamical regimes. For fluid vesicles, we predict that at small shear rates thermal fluctuations induce a tumbling motion for any viscosity contrast. For elastic capsules, due to thermal mixing, an intermittent regime appears in regions where deterministic models predict only pure tank treading or tumbling.