The present paper introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly oriented rectangles. By conducting extensive simulations, we report high-precision percolation thresholds for a variety of homogeneous systems with different rectangle aspect ratios. This paper verifies and extends the excluded area theory. It is confirmed that percolation thresholds are dominated by the average excluded areas for both homogeneous and heterogeneous rectangle systems (except for some special heterogeneous systems where the rectangle lengths differ too much from one another). In terms of the excluded areas, generalized formulas are proposed to effectively predict precise percolation thresholds for all these rectangle systems. This paper is, therefore, helpful for both practical applications and theoretical studies concerning relevant systems.

The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit.

We report on the reptation of vertically vibrated droplets of fine particles lying on a solid incline. On the one hand, time-resolved measurements show that the gas pressure in the gap between the droplet bottom and the solid surface can be accounted for by a Darcy law. The cumulative effect of the viscous drag is responsible for the droplet formation. On the other hand, we show that the gap pressure is responsible for an effective horizontal acceleration whose cumulative effect is the upward reptation of the droplets. Using various geometries of the solid substrate, we manipulate the droplets and study the effects of the substrate geometry and of the experimental parameters on the droplet shape and dynamics. The experimental results are discussed in the light of theoretical arguments. This study demonstrates that, by the choice of a suitable geometry of the surface and characteristics of the vibration, one can develop tools for precise powder handling and control.

Microtubules supported by surrounding cross linkers in eukaryotic cells can bear a much higher compressive force than free-standing microtubules. Different from some previous studies, which treated the surroundings as a continuum elastic foundation or elastic medium, the present paper develops a micromechanics numerical model to examine the role of randomly distributed discrete cross linkers in the buckling of compressed microtubules. First, the proposed numerical approach is validated by reproducing the uniform multiwave buckling mode predicted by the existing elastic-foundation model. For more realistic buckling of microtubules surrounded by randomly distributed cross linkers, the present numerical model predicts that the buckling mode is localized at one end in agreement with some known experimental observations. In particular, the critical force for localized buckling, predicted by the present model, is insensitive to microtubule length and can be about 1 order of magnitude lower than those given by the elastic-foundation model, which suggests that the elastic-foundation model may have overestimated the critical force for buckling of microtubules in vivo. In addition, unlike the elastic-foundation model, the present model can capture the effect of end conditions on the critical force and wavelength of localized buckling. Based on the known data of spacing and elastic constants of cross linkers available in literature, the critical force and wavelength of the localized buckling mode, predicted by the present model, are compared to some experimental data with reasonable agreement. Finally, two empirical formulas are proposed for the critical force and wavelength of the localized buckling of microtubules surrounded by cross linkers.

Inspired by RecA-protein-based homology recognition, we consider the pairing of two long linear arrays of binding sites. We propose a fully reversible, physically realizable biased random walk model for rapid and accurate self-assembly due to the spontaneous pairing of matching binding sites, where the statistics of the searched sample are included. In the model, there are two bound conformations, and the free energy for each conformation is a weakly nonlinear function of the number of contiguous matched bound sites.

Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features by providing a molecular-scale mechanism for energy dissipation. One example is in the polymeric glue connection between collagen fibrils in animal bone. In this paper we propose a simple kinetic model that describes the breakage of sacrificial bonds and the release of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation. This enables us to predict the mechanical behavior of a quasi-one-dimensional ensemble of polymers at different stretching rates. We find that both the rupture peak heights and maximum stretching distance increase with the stretching rate. In addition, our theory naturally permits the possibility of self-healing in such biological structures.

We study the dynamics of a relativistic charged particle in the presence of a uniform magnetic field and a stationary electrostatic wave that propagates at an arbitrary angle. The wave is considered as a series of periodic pulses which allows us to derive an exact map for the system. In particular, we investigate the heating process of an initially low-energy particle. It is found that abrupt changes in the maximum energy attained by the particle may occur as the angle between the wave propagation and the magnetic field varies. To determine what is the mechanism behind this phenomenon a reduced Hamiltonian that retains the important dynamical features is obtained. Using both Poincaré plots and perturbation theory, we identify that a separatrix reconnection is the key mechanism for the abrupt change in particle response.

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

We collect results for bond percolation on various lattices from two to fourteen dimensions that, in the limit of large dimension $d$ or number of neighbors $z$, smoothly approach a randomly diluted Erdős-Rényi graph. We include results on bond-diluted hypersphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis, and skewness evolving smoothly with dimension towards the Erdős-Rényi limit.

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature $T$, packing fraction $\varphi$, and uniform applied shear strain rate $\dot{\gamma }$. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters $\varphi$ and $T/\dot{\gamma }$. Here $T/\dot{\gamma }\to 0$ defines the athermal limit in which a shear-driven jamming transition occurs at a well defined ${\varphi }_J$ and $T/\dot{\gamma }\to \infty$ defines the thermalized limit where an equilibrium glass transition may take place at ${\varphi }_G$. This conclusion argues that athermal jamming and equilibrium glassy behavior are not controlled by the same critical point. Preliminary results suggest ${\varphi }_G<{\varphi }_J$.

We study the temperature field and the resulting flow pattern in the vicinity of a heated metal-capped Janus particle. If its thickness exceeds about 10 nm, the cap forms an isotherm and the flow pattern comprises a quadrupolar term that decays with the square of the inverse distance $\sim$$r^{-2}$. For much thinner caps the velocity varies as $\sim$$r^{-3}$. These findings could be relevant for collective effects in dense suspensions and for the circular tracer motion observed recently in the vicinity of a tethered Janus particle.

Dielectric relaxation spectra of a liquid crystalline (LC) material showing blue-phase-III (BPIII) for a considerably large temperature regime consisting of T-shaped molecules are investigated. A low frequency relaxation mode is observed in the isotropic phase ($I$) as well as in BPIII of the investigating material which is attributed to the short axis rotation of the T-shaped molecules. The outcome of the temperature and dc bias field variation of dielectric strength (Δε) and relaxation frequency (${\nu }_c$) in the vicinity of the $I$-BPIII transition is also discussed. The temperature dependence of ${\nu }_c$ in BPIII with a minor deviation from Arrhenius activities in the fluctuation-dominated nonlinear region (FDNLR) is found to follow the unusual thermal behavior of the activation energy ($E_A$). The growth of pretransitional fluctuations is found to be nonlinear in the vicinity of the $I$-BPIII transition. A moderate growth of transition fluctuation commences from the value of the exponent ${\alpha }_{\mathrm{eff}}=0.38$/°C, which is obtained by an exponential variation of ${\nu }_c$ with respect to temperature in BPIII. Observed dynamic phenomenon in the vicinity of the $I$-BPIII transition regions is explained on the basis of the Landau–de Gennes and Maier-Saupe Theories.

We study a simple bead-spring polymer model exhibiting competing crystallization and glass transitions. Constant-pressure molecular dynamics simulations are employed to study phase behavior and morphological order. For adequately slow quench rates, chain systems exhibit a first-order phase transition (crystallization) below a critical temperature $T=T_{\mathrm{cryst}}$. We observe the formation of close-packed crystallites of FCC and/or HCP order, separated by domain walls, twin defects, and amorphous regions. Such crystal structures closely resemble the corresponding ordered morphologies of athermal polymer packings: fully flexible chains retain random-walk-like configurations in the crystalline state and do not form lamellae, while semiflexible chains do form lamellae. The model presented here is well suited to the modeling of granular and colloidal polymers, in particular for elucidating the factors that dictate the formation of specific ordered morphologies.

Colloidal particles located close to the surface of an acoustic thickness shear resonator feel an attractive steady force, which is induced by the high-frequency tangential motion of the resonator surface. The range of the force is about half the penetration depth of the transverse viscous wave, that is, half of the thickness of the Stokes boundary layer. For an oscillation amplitude of 10 nm and a particle radius of 100 nm, the depth of attractive potential well corresponds to about 3 times the thermal energy, $k_{B}T$. The force therefore suffices to overcome Brownian motion.

We show that the actual diffusive dynamics, governing the momentum relaxation of a polymer molecule, and described by a Fokker-Planck equation, may be replaced by a BGK-type relaxation dynamics without affecting the slow (Smoluchowski) dynamics in configuration space. Based on the BGK-type description, we present a lattice-Boltzmann (LB) based direct discretization approach for the phase-space description of inertial polymer dynamics. We benchmark this formulation by determining the bulk rheological properties for both steady and time-dependent shear and extensional flows at moderate to large Weissenberg numbers. Finally, we compare the usefulness of the different discrete velocity models, typically used in the LB framework, for solving diffusive dynamics based on the Fokker-Planck equation.

We investigate the correlation functions of mesoscopic electronic transport in open chaotic quantum dots with finite tunnel barriers in the crossover between Wigner-Dyson ensembles. Using an analytical stub formalism, we show the emergence of a depletion and amplification of conductance fluctuations as a function of tunnel barriers for both parametric variations of electron energy and magnetoconductance fields. Furthermore, even for pure Dyson ensembles, correlation functions of conductance fluctuations in chaotic quantum dots can exhibit anticorrelation. Experimental support to our findings is pointed out.

Monte Carlo simulation, experiment, and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and planar alignment. It is shown that the easy axis and effective anchoring energy promoted by such surfaces can be readily controlled by adjusting the design of the pattern. The calculations reveal rich behavior: for strong anchoring, as exhibited by the simulated system, for rectangle ratios $\ge 2$ the nematic aligns in the direction of the long edge of the rectangles, the azimuthal anchoring coefficient changing with pattern shape. In weak anchoring scenarios, however, including our experimental systems, preferential anchoring is degenerate between the two rectangle diagonals. Bistability between diagonally aligned and edge-aligned arrangement is predicted for intermediate combinations of anchoring coefficient and system length scale.

Electrochemical gating is the process by which an electric field normal to the insulator electrolyte interface shifts the surface chemical equilibrium and further affects the charge in solution [Jiang and Stein, Langmuir 26, 8161 (2010)]. The surface chemical reactivity and double-layer charging at the interface of electrolyte-oxide-semiconductor (EOS) capacitors is investigated. We find a strong $p$H-dependent hysteresis upon dc potential cycling. Varying salinity at a constant $p$H does not change the hysteretic window, implying that field-induced surface $p$H regulation is the dominant cause of hysteresis. We propose and investigate this mechanism in foundry-made floating-gate ion-sensitive field-effect transistors, which can serve as both an ionic sensor and an actuator. Termed the chemoreceptive neuron metal-oxide-semiconductor (CνMOS) transistor, it features independently driven control gates (CGs) and sensing gates (SGs) that are capacitively coupled to an extended floating gate (FG). The SG is exposed to fluid, the CG is independently driven, and the FG is capable of storing charge $Q_{FG}$ of either polarity. Asymmetric capacitive coupling between the CG and SG to FG results in intrinsic amplification of the measured surface potential shifts and influences the FG charge injection mechanism. This modified SG surface condition was monitored through transient recordings of the output current, performed under alternate positive and negative CG pulses. Transient recordings revealed a hysteresis where the current was enhanced under negative pulsing and reduced after positive pulsing. This hysteresis effect is similar to that observed with EOS capacitors, suggesting a field-dependent surface charge regulation mechanism at play. At high CG biases, nonvolatile charge $Q_{FG}$ tunneling into the FG occurs, which creates a larger field and tunes the $p$H response and the point of zero charge. This mechanism gives rise to surface programmability. In this paper we describe the operational principles, tunneling mechanism, and role of electrolyte composition under field modulation. The experimental findings are then modeled by a Poisson-Boltzmann formulation with surface $p$H regulation. We find that surface ionization constants play a dominant role in determining the $p$H tuning effect. In the following paper [K. Jayant et al., Phys. Rev. E 88, 012802 (2013)] we extend the dual-gate operation to molecular sensing and demonstrate the use of $Q_{FG}$ to achieve manipulation of surface-adsorbed DNA.

The chemoreceptive neuron metal-oxide-semiconductor transistor described in the preceding paper is further used to monitor the adsorption and interaction of DNA molecules and subsequently manipulate the adsorbed biomolecules with injected static charge. Adsorption of DNA molecules onto poly-L-lysine–coated sensing gates (SGs) modulates the floating gate (FG) potential ${\psi }_{\mathrm{O}}$, which is reflected as a threshold voltage shift measured from the control gate (CG) $V_{\mathrm{th}\_\mathrm{CG}}$. The asymmetric capacitive coupling between the CG and SG to the FG results in $V_{\mathrm{th}\_\mathrm{CG}}$ amplification. The electric field in the SG oxide $E_{\mathrm{SG}\_\mathrm{ox}}$ is fundamentally different when we drive the current readout with $V_{\mathrm{CG}}$ and $V_{\mathrm{ref}}$ (i.e., the potential applied to the CG and reference electrode, respectively). The $V_{\mathrm{CG}}$-driven readout induces a larger $E_{\mathrm{SG}\_\mathrm{ox}}$, leading to a larger $V_{\mathrm{th}\_\mathrm{CG}}$ shift when DNA is present. Simulation studies indicate that the counterion screening within the DNA membrane is responsible for this effect. The DNA manipulation mechanism is enabled by tunneling electrons (program) or holes (erase) onto FGs to produce repulsive or attractive forces. Programming leads to repulsion and eventual desorption of DNA, while erasing reestablishes adsorption. We further show that injected holes or electrons prior to DNA addition either aids or disrupts the immobilization process, which can be used for addressable sensor interfaces. To further substantiate DNA manipulation, we used impedance spectroscopy with a split ac-dc technique to reveal the net interface impedance before and after charge injection.