Single-beam oscillating optical tweezers can be used to trap rod-shaped bacterial cells and align them with their long axis lying within the focal plane. While such configuration is useful for imaging applications, the corresponding imaging resolution is limited by the fluctuations of the trapped cell. We study the fluctuations of four of the coordinates of the trapped cell, two for its center of mass position and two for its angular orientation, showing the way they depend on the trap length and the trapping beam power. We find that optimal trapping stability is obtained when the trap length is about the same as the cell length and that cell fluctuations in the focal plane decrease like the inverse of the trapping power.

We report the formation mechanism of a unique pattern observed in ac-driven electroconvection of nematic liquid crystals (NLCs), in which many well-organized grid cells are very regularly aggregated in a two-dimensional plane, globally forming a nearly perfect grid pattern (GP). Intuitively, the formation of such a pattern is unpredictable; usually, the perfectly regular normal roll (NR) showing a preferred roll direction is observed in this system by imposing a fixed initial direction of an NLC. The GP was investigated by varying the ac voltage and frequency. To characterize the GP, the density ${\rho }_{\mathrm{GP}}$, the width $a$ and length $b$ of the grids, and the oscillation period $T_{\mathrm{GP}}$ of an inner optical pattern of the grids were measured; moreover, the lengths ${\overline{L}}_x$ and ${\overline{L}}_y$ characterizing phase-jump lines (PJLs) in the GP were examined. By taking into account the process of evolution from a fluctuating NR with defects to the GP, the velocity and director fields of the GP are estimated. Furthermore, in comparison with the bimodal mechanism proposed in the earlier study, a possible mechanism for the GP formed by the PJLs is discussed; various routes to GPs depending on the ac frequency are proposed.

This article presents an analysis of the shear strength of numerical samples composed of polyhedra presenting a grain size dispersion. Previous numerical studies using, for instance, disks, polygons, and spheres, have consistently shown that microstructural properties linked to the fabric and force transmission allow granular media to exhibit a constant shear resistance although packing fraction can dramatically change as a broader grain-size distribution is considered. To have a complete picture of such behavior, we developed a set of numerical experiments in the frame of the discrete element method to test the shear strength of polydisperse samples composed of polyhedral grains. Although the contact networks and force transmission are quite more complex for such generalized grain shape, we can verify that the shear strength independence still holds up for 3D regular polyhedra. We make a particular focus upon the role of different contact types in the assemblies and their relative contributions to the granular connectivity and sample strength. The invariance of shear strength at the macroscopic scale results deeply linked to fine compensations at the microstructural level involving geometrical and force anisotropies of the assembly.

This article investigates phonons and elastic response in randomly diluted lattices constructed by combining (via the addition of next-nearest bonds) a twisted kagome lattice, with bulk modulus $B=0$ and shear modulus $G>0$, with either a generalized untwisted kagome lattice with $B>0$ and $G>0$ or with a honeycomb lattice with $B>0$ and $G=0$. These lattices exhibit jamming-like critical endpoints at which $B, G$, or both $B$ and $G$ jump discontinuously from zero while the remaining moduli (if any) begin to grow continuously from zero. Pairs of these jamming points are joined by lines of continuous rigidity percolation transitions at which both $B$ and $G$ begin to grow continuously from zero. The Poisson ratio and $G/B$ can be continuously tuned throughout their physical range via random dilution in a manner analogous to “tuning by pruning” in random jammed lattices. These lattices can be produced with modern techniques, such as three-dimensional printing, for constructing metamaterials.

The transverse fracture of model unidirectional composite specimen, comprising up to $2^{20}$ fibers with random strengths, is studied using Monte Carlo simulations. The load sharing from broken to intact fibers is assumed to obey power-law scaling $\sim r^{-\gamma }$ with distance $r$ from the fiber break. Fiber breaks are assumed to interact in order to remain traction free. The pattern of fiber breaks that propagate catastrophically is interpreted through cluster analysis. The empirical strength distributions obtained from the simulations are interpreted using two probabilistic models of brittle fracture available in the literature. These point to a transition from the brittle to the tough fracture mode as $\gamma \downarrow 2$. The transitional $\gamma$ is approximately equal to that reported in the literature for noninteracting fiber breaks.

The interaction of dielectric barrier discharge plasma and silicone-oil liquid droplet in a Hele-Shaw cell was investigated experimentally employing synchronized optical and electrical time-resolved measurements. Temporal development of the destabilization, stretching, and fragmentation of the plasma-liquid interface was studied for the whole event lifespan. The perturbation wavelength and temporal development of fingering speed, plasma-liquid interface length, mean transferred charge, and fractal dimension of the pattern were determined. Recorded changes in the dissipated mean power show a strong correlation to subsequent stretching of the interface, opening new methodological possibilities for future investigations. Our extensive parametric study shows that oil viscosity and applied voltage amplitude both have a significant impact on the interface evolution. Notably, at relatively high voltages the destabilized interface featured properties noticeably diverging from the theoretical prediction of a known model. We propose an explanation based on the change of the liquid viscosity with increased heating at high applied voltage amplitudes.

A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the one-dimensional hydrodynamic code LILAC for planar and spherical targets. At present, the initial plasma formation during the early stages of a laser drive are modeled in an ad hoc manner, until the formation of a critical surface. Implementation of the physics-based models predict higher values of electron temperature and pressure than the ad hoc model. Moreover, the numerical predictions are consistent with previous experimental observations of the shinethrough mechanism in plastic ablators. For planar targets, a decompression of the rear end of the target was observed that is similar to recent experiments. An application of this model is to understand the laser-imprint mechanism that is caused by nonuniform laser irradiation due to single beam speckle.

In order to increase the accuracy of temporal solutions, reduce the computational cost of time marching, and improve the stability associated with collisions for the finite-volume discrete Boltzmann method, an advanced implicit Bhatnagar-Gross-Krook (BGK) collision model using a semi-Lagrangian approach is proposed in this paper. Unlike existing models, in which the implicit BGK collision is resolved either by a temporal extrapolation or by a variable transformation, the proposed model removes the implicitness by tracing the particle distribution functions (PDFs) back in time along their characteristic paths during the collision process. An interpolation scheme is needed to evaluate the PDFs at the traced-back locations. By using the first-order interpolation, the resulting model allows for the straightforward replacement of $f_{\alpha }^{\mathrm{eq},n+1}$ by $f_{\alpha }^{\mathrm{eq},n}$ no matter where it appears. After comparing the proposed model with the existing models under different numerical conditions (e.g., different flux schemes and time-marching schemes) and using the proposed model to successfully modify the variable transformation technique, three conclusions can be drawn. First, the proposed model can improve the accuracy by almost an order of magnitude. Second, it can slightly reduce the computational cost. Therefore, the proposed scheme improves accuracy without extra cost. Finally, the proposed model can significantly improve the $\mathrm{\Delta }t/\tau$ limit compared to the temporal interpolation model while having the same $\mathrm{\Delta }t/\tau$ limit as the variable transformation approach. The proposed scheme with a second-order interpolation is also developed and tested; however, that technique displays no advantage over the simple first-order interpolation approach. Both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first-order interpolation can outperform the same scheme with second-order interpolation, as well as the existing temporal extrapolation and variable transformation schemes.

A mean-field theory is introduced to describe heliconical nematic ($N_{\text{TB}}$), heliconical $\text{smectic-}C$ ($S_m{C}_{\text{TB}}$), and biaxial heliconical $\text{smectic-}C$ ($S_m{C}_{\text{TB},b}$) phases with mirror symmetry breaking. We extend our previous theories of the $N_{TB}$ phase to the heliconical $\text{smectic-}C$ phases, by taking into account one-dimensional spatial ordering of smectic layers. The calculated phase diagrams on the temperature–alkyl chain length plane show a rich variety of phase transitions: first- and second-order $N_{\text{TB}}\text{−}{S}_m{C}_{\text{TB}}$ transitions, etc., including tricritical, tetracritical, and multicritical points. Our theory is qualitatively consistent with an experimental phase diagram.

The Euler characteristic $\chi =\left|V\right|-\left|E\right|$ and the total length $\mathcal{L}$ are the most important topological and geometrical characteristics of a metric graph. Here $\left|V\right|$ and $\left|E\right|$ denote the number of vertices and edges of a graph. The Euler characteristic determines the number $\beta$ of independent cycles in a graph while the total length determines the asymptotic behavior of the energy eigenvalues via Weyl's law. We show theoretically and confirm experimentally that the Euler characteristic can be determined (heard) from a finite sequence of the lowest eigenenergies ${\lambda }_1,...,{\lambda }_N$ of a simple quantum graph, without any need to inspect the system visually. In the experiment quantum graphs are simulated by microwave networks. We demonstrate that the sequence of the lowest resonances of microwave networks with $\beta \le 3$ can be directly used in determining whether a network is planar, i.e., can be embedded in the plane. Moreover, we show that the measured Euler characteristic $\chi$ can be used as a sensitive revealer of the fully connected graphs.

We study a two-dimensional system of magnetic particles under an alternating magnetic field. The particles are settled on the surface of a negative lens where they tend to sediment toward the center due to gravity. The effective temperature is controlled by the intensity of the applied magnetic field. The system is cooled down from a gaslike state to a solidlike state at different rates. We observe that for some slow cooling rates the final configuration of system is a hexagonal compact arrange, while for the faster cooling rates the final configurations are glasslike states. We followed the time evolution of the system, which allows us to determine in detail changes in quantities such as the interparticle distance. We determine the glass transition temperature for different cooling rates, finding that such temperature increases as the cooling rate decreases, in contrast with some other glass-forming liquids.

We study the dynamics of a particle in a fluid from a generalized Langevin equation (GLE) with a frictional exponential memory kernel and hydrodynamic interactions. By using Laplace analysis we obtain the analytical expressions for the velocity autocorrelation function (VACF) and mean square displacement (MSD) of the particle. Our results show that, in the strictly asymptotic time limit, the dynamics of the particle correspond to a particle ruled by a GLE with a Dirac delta friction memory kernel and hydrodynamic interactions. However, at intermediate times the dynamical behavior is qualitatively different due to the presence of a characteristic time in the frictional exponential memory kernel. Remarkably, the VACF exhibits oscillations and negative correlation regimes which are reminiscent of features already observed in pioneering works of molecular dynamics simulations. Moreover, ripples in the MSD appear as an emerging behavior associated with the mentioned regimes.

We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude ${\left|s\right|}^2$ under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, ${\left|s\right|}^2$ shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in ${\left|s\right|}^2$. However, the ${\left|s\right|}^2$ maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.

The Axelrod model has been widely studied since its proposal for social influence and cultural dissemination. In particular, the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters, $F$ and $Q$. In this work, we show that the Axelrod model undergoes a second-order phase transition in the limit of $F\to \infty$ on a complete graph. This transition is equivalent to the Erdős-Rényi phase transition in random networks when it is described in terms of the probability of interaction at the initial state, which depends on a scaling relation between $F$ and $Q$. We also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter $F$.

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1–C4 and I1–I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

In the study of randomly connected neural network dynamics there is a phase transition from a simple state with few equilibria to a complex state characterized by the number of equilibria growing exponentially with the neuron population. Such phase transitions are often used to describe pathological brain state transitions observed in neurological diseases such as epilepsy. In this paper we investigate how more realistic heterogeneous network structures affect these phase transitions using techniques from random matrix theory. Specifically, we parametrize the network structure according to Dale's law and use the Kac-Rice formalism to compute the change in the number of equilibria when a phase transition occurs. We also examine the condition where the network is not balanced between excitation and inhibition causing outliers to appear in the eigenspectrum. This enables us to compute the effects of different heterogeneous network connectivities on brain state transitions, which can provide insights into pathological brain dynamics.

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

The extracellular matrix (ECM) has a fiber network that provides physical scaffolds to cells and plays important roles by regulating cellular functions. Some previous works characterized the mechanical and geometrical properties of the ECM fiber network using reconstituted collagen-I. However, the characterization of the porous structure of reconstituted collagen-I has been limited to the pore diameter measurement, and pore network extraction has not been applied to reconstituted collagen-I despite the importance of pore interconnectivity. Here, we aim to show the importance of characterizing the pore network of reconstituted collagen-I by comparing the pore networks of structures that have different fiber alignments. We show that the fiber alignment significantly changes the pore throat area but not the pore diameter. Also, we demonstrate that larger pore throats are directed in the direction of the fiber alignment, which may help in understanding the enhanced cell migration when fibers are aligned.

In this paper, based on the numerical calculation of total energy utilizing the Green's function method, we investigate how a field-triggered vertical positional transition of a microparticle suspended in a nematic liquid crystal cell is influenced by the direction of the applied field, surface anchoring feature, and nematic's dielectric properties. The new equilibrium position of the translational movement is decided via a competition between the buoyant force and the effective force built on the microparticle by the elastic energy gradient along the vertical direction. The threshold value of external field depends on thickness $L$ and Frank elastic constant $K$ and slightly on the microparticle size and density, in a Fréedericksz-like manner, but by a factor. For a nematic liquid crystal cell with planar surface alignment, a bistable equilibrium structure for the transition is found when the direction of the applied electric field is (a) perpendicular to the two plates of the cell with positive molecular dielectric anisotropy or (b) parallel to the two plates and the anchoring direction of the cell with negative molecular dielectric anisotropy. When the electric field applied is parallel to both plates and perpendicular to the anchoring direction, the microparticle suspended in the nematic liquid crystal tends to be trapped in the midplane, regardless of the sign of the molecular dielectric anisotropy. Such a phenomenon also occurs for negative molecular dielectric anisotropy if the external field is applied perpendicular to the two plates. Explicit formulas proposed for the critical electric field agree extremely well with the numerical calculation.