High-resolution ac calorimetry has been used to study the nematic to smectic-$A$ $\left(N\text{−}\mathrm{Sm}A\right)$ phase transition in the liquid crystal octylcyanobiphenyl (8CB) confined in aligned colloidal aerosil gels. A stable and robust nematic alignment was achieved by repeated thermal cycling of the samples in the presence of a strong uniform magnetic field. In some ways (such as transition temperature and integrated enthalpy), the dependence of the specific heat peak associated with the $N\text{−}\mathrm{Sm}A$ transition on the aerosil density for aligned gels is consistent with that observed in unaligned (random) gel samples. However, a power-law analysis reveals that the behavior of the critical exponent $\alpha$ is quite different. For random gels, $\alpha$ varies gradually with aerosil density, whereas we find that $\alpha$ for aligned gels shifts abruptly to an $XY$-like value for the lowest aerosil density studied and remains essentially constant as the sil density increases. This aerosil density independence of $\alpha$ is consistent with the critical behavior of the smectic correlation lengths obtained from an x-ray scattering study of 8CB in aligned aerosil gels. The combined calorimetric and x-ray results indicate that the role of quenched randomness in aligned gels of $8\mathrm{CB}+\text{sils}$ differs significantly from that in random gels.

In an evoked magnetic field of magnetoencephalography a wave form is calculated by averaging. We propose that the wave form is deterministic in the case of $5\mathrm{Hz}$ periodical stimuli. We have found with statistical accuracy that the wave form of a somatosensory evoked magnetic field is deterministic in $5\mathrm{Hz}$ periodical median nerve stimuli, since any stationary process is decomposed into a deterministic part and a nondeterministic part from the Wold decomposition theorem. For the decorrelation method of blind source separation we have obtained several components which have nonzero wave forms. Via the selected components time series data of a somatosensory evoked magnetic field generated from somatosensory cortexes have been separated from background brain noise by using a $T∕k$ (fractional) type decorrelation method.

We study the influence of noisy transcription factor signals on cis-regulatory promoter elements. These elements process the probability of binary binding events analogous to computer logic gates. At equilibrium, this probability is given by the so-called input function. We show that transcription factor noise causes deviations from the equilibrium value due to the nonlinearity of the input function. For a single binding site, the correction is always negative resulting in an occupancy below the mean-field level. Yet for more complex promoters it depends on the correlation of the transcription factor signals and the geometry of the input function. We present explicit solutions for the basic types of AND and OR gates. The correction size varies among these different types of gates and signal types, mainly being larger in AND gates and for correlated fluctuations. In all cases we find excellent agreement between the analytical results and numerical simulations. We also study the E. coli Lac operon as an example of an AND NOR gate. We present a consistent mathematical method that allows one to separate different sources of noise and quantifies their effect on promoter occupation. A surprising result of our analysis is that Poissonian molecular fluctuations, in contrast to external fluctuations, do no contribute to the correction.

Thermodynamic length is a path function that generalizes the notion of length to the surface of thermodynamic states. Here, we show how to measure thermodynamic length in far-from-equilibrium experiments using the work fluctuation relations. For these microscopic systems, it proves necessary to define the thermodynamic length in terms of the Fisher information. Consequently, the thermodynamic length can be directly related to the magnitude of fluctuations about equilibrium. The work fluctuation relations link the work and the free-energy change during an external perturbation on a system. We use this result to determine equilibrium averages at intermediate points of the protocol in which the system is out of equilibrium. This allows us to extend Bennett’s method to determine the potential of the mean force, as well as the thermodynamic length, in single-molecule experiments.

By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few distant agents, namely, pseudoleaders. The leader can directly affect the pseudoleaders, thereby influencing all the other agents through them efficiently. Moreover, these pseudoleaders are able to predict the leader’s motion several steps ahead and use this information in decision making towards coherent flocking with more stable formation. It is shown that drastic improvement can be achieved in terms of both the consensus performance and the communication cost. From the engineering point of view, the current protocol allows for a significant improvement in the cohesion and rigidity of the formation at a fairly low cost of adding a few long-range links embedded with predictive capabilities. Significantly, this work uncovers an important feature of flocks that predictive capability and long-range links can compensate for the insufficiency of each other. These conclusions are valid for both the attractive and repulsive swarm model and the Vicsek model.

We report the results of a series of current scaling experiments with the $Z$ accelerator for the compact, single, $20\text{−}\mathrm{mm}$ diameter, $10\text{−}\mathrm{mm}$ long, tungsten-wire arrays employed for the double-ended hohlraum ICF concept [M. E. Cuneo et al., Plasma Phys. Controlled Fusion 48, R1 (2006)]. We measured the $z$-pinch peak radiated x-ray power and total radiated x-ray energy as a function of the peak current, at a constant implosion time ${\tau }_{\mathrm{imp}}=80\mathrm{ns}$. Previous x-ray emission current scaling for these compact arrays was obtained at ${\tau }_{\mathrm{imp}}=95\mathrm{ns}$ in the work of Stygar et al. [Phys. Rev. E 69, 046403 (2004)]. In the present study we utilized lighter single-tungsten-wire arrays. For all the measurements, the load hardware dimensions, materials, and array wire number $(N=300)$ were kept constant and were the same as the previous study. We also kept the normalized load current spatial and temporal profiles the same for all experiments reported in this work. Two different currents, $11.2\pm 0.2\mathrm{MA}$ and $17.0\pm 0.3\mathrm{MA}$, were driven through the wire arrays. The average peak x-ray power for these compact wire arrays increased by $26\%\pm 7\%\text{to}158\pm 26\mathrm{TW}$ at $17\pm 0.3\mathrm{MA}$ from the $125\pm 24\mathrm{TW}$ obtained at a peak current of $18.8\pm 0.5\mathrm{MA}$ with ${\tau }_{\mathrm{imp}}=95\mathrm{ns}$. The higher peak power of the faster implosions may possibly be attributed to a higher implosion velocity, which in turn improves the implosion stability, and/or to shorter wire ablation times, which may lead to a decrease in trailing mass and trailing current. Our results show that the scaling of the radiated x-ray peak power and total radiated x-ray energy scaling with peak drive current to be closer to quadratic than the results of Stygar et al. We find that the x-ray peak radiated power is $P_r\propto I^{1.57\pm 0.20}$ and the total x-ray radiated energy $E_r\propto I^{1.9\pm 0.24}$. We also find that the current scaling exponent of the power is sensitive to the inclusion of a single data point with a peak power at least $1.9\sigma$ below the average. If we eliminate this particular shot from our analysis (shot 1608), the power and energy scaling becomes closer to quadratic. Namely, we find that the dependence on the peak load current of the peak x-ray radiated power and the total x-ray radiated energy become $P_r\propto I^{1.71\pm 0.10}$ and $E_r\propto I^{2.01\pm 0.21}$, respectively. In this case, the power scaling exponent is different by more than $2\sigma$ from the previously published results of Stygar et al. Larger data sets are likely required to resolve this uncertainty and eliminate the sensitivity to statistical fluctuations in any future studies of this type. Nevertheless, with or without the inclusion of shot 1608, our results with ${\tau }_{\mathrm{imp}}=80\mathrm{ns}$ fall short of an ${\mathit{I}}^2$ scaling of the peak x-ray radiated power by at least $2\sigma$. In either case, the results of our study are consistent with the heuristic wire ablation model proposed by Stygar et al. $(P_r\propto I^{1.5})$. We also derive an empirical predictive relation that connects the power scaling exponent with certain array parameters.

We report on the crystal growth scenario in gravity-matched, polydisperse hard-sphere-like colloids at increasing particle concentration. In the fluid-crystal coexistence region, the crystal size as a function of time shows two separate regimes corresponding to crystal growth and crystal ripening. At higher supersaturation the crystal size grows according to the same power law through the whole experimental window of a few days: crystal growth and ripening merge together. We show that our observations cannot be explained by considering the slowing down of single-particle dynamics due to increasing volume fraction. We suggest that size fractionation occurring at the crystal-fluid interface is the dominant mechanism.

A perturbation strategy is proposed which allows liquid perturbation methodology to be applied to extremely low temperature situations for which the available liquid integral equation theory and traditional thermodynamic perturbation theory fail. The possibility of avoiding the low temperature problem of the thermodynamic perturbation theory not only is of relevance to the investigation of complex fluids, but also may be useful for reformulation of other liquid theories to achieve higher accuracy and avoid the respective low temperature problems.

It is shown that in a cluster of many colloids, trapped at a liquid-air interface, the well-known vertical-force-induced pairwise logarithmic attraction changes to a strongly enhanced power-law attraction. In large two-dimensional clusters, the attraction energy scales as the inverse square of the distance between colloids. The enhancement is given by the ratio $\eta =\left(\text{square}\text{of}\text{the}\text{capillary}\text{length}\right)$/(interface surface area per colloid) and can be as large as ${10}^5$. This explains why a very small vertical force on colloids, which is too weak to bring two of them together, can stabilize many-body structures on a liquid-air interface. The profile of a cluster is shown to consist of a large slow collective envelope modulated by a fast low-amplitude perturbation due to individual colloids. A closed equation for the slow envelope, which incorporates an arbitrary power-law repulsion between colloids, is derived. For example, this equation is solved for a large circular cluster with the hard-core colloid repulsion. It is suggested that the predicted effect is responsible for mysterious stabilization of colloidal structures observed in experiments on a surface of isotropic liquid and nematic liquid crystal.

Intracellular transport of DNA carriers is a fundamental step of gene delivery. By combining both theoretical and numerical approaches we study here single and several viruses and DNA particles trafficking in the cell cytoplasm to a small nuclear pore. We present a physical model to account for certain aspects of cellular organization, starting with the observation that a viral trajectory consists of epochs of pure diffusion and epochs of active transport along microtubules. We define a general degradation rate to describe the limitations of the delivery of plasmid or viral particles to a nuclear pore imposed by various types of direct and indirect hydrolysis activity inside the cytoplasm. By replacing the switching dynamics by a single steady state stochastic description, we obtain estimates for the probability and the mean time for the first one of many particles to go from the cell membrane to a small nuclear pore. Computational simulations confirm that our model can be used to analyze and interpret viral trajectories and estimate quantitatively the success of nuclear delivery.

We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hückel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling, in agreement with the numerical results.

We explore experimentally the fluidization of vertically agitated polymethylmethacrylate spheres wetted by liquid ${}^4\mathrm{He}$. By controlling the temperature around the $\lambda$ point, we change the properties of the wetting liquid from a normal fluid (helium I) to a superfluid (helium II). For wetting by helium I, the critical acceleration for fluidization $\left({\Gamma }_c\right)$ shows a steep increase close to the saturation of the vapor pressure in the sample cell. For helium II wetting, ${\Gamma }_c$ starts to increase at about 75% saturation, indicating that capillary bridges are enhanced by the superflow of the unsaturated helium film. Above saturation, ${\Gamma }_c$ enters a plateau regime where the capillary force between particles is independent of the bridge volume. The plateau value is found to vary with temperature and shows a peak at $2.1\mathrm{K}$, which we attribute to the influence of the specific heat of liquid helium.

Charged colloidal particles interact via a hard core Yukawa potential, while isotropic Lennard-Jones-like potentials are frequently used as pair potentials in metals. We present measurements of the structure factor of shear molten monodisperse colloids and molten metals using ultrasmall-angle x-ray scattering and elastic neutron scattering, respectively. In both systems data analysis gives evidence of fivefold-symmetric short-range order becoming more pronounced with increasing deviations from equilibrium. The experiments demonstrate that in both systems topological effects control ordering in the melt state.

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range $L=20–100$ via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the two-dimensional Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with $\nu =1.30\left(6\right)$ and $\beta ∕\nu =0.128\left(5\right)$. These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems with and without quenched disorder. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.

We report simulations of a two-dimensional, dense, bidisperse system of inelastic hard disks falling down a vertical tube under the influence of gravity. We examine the approach to jamming as the average flow of particles down the tube is slowed by making the outlet narrower. Defining coarse-grained velocity and stress fields, we study two-point temporal and spatial correlation functions of these fields in a region of the tube where the time-averaged velocity is spatially uniform. We find that fluctuations in both velocity and stress become increasingly correlated as the system approaches jamming. We extract a growing length scale and time scale from these correlations.

The electromechanical behavior of a gas-fluidized bed of insulating silica nanoparticles is investigated. When fluidized by gas, these nanoparticles form highly porous agglomerates of size of the order of hundreds of microns, which gives rise to a nonbubbling fluidization regime. Bed expansion is enhanced by an imposed alternating electric field for oscillation frequencies in the range between tens and hundreds of hertzs and field strengths of about $1\mathrm{kV}∕\mathrm{cm}$. Nanoparticle agglomerates are naturally charged and experience forced oscillations that cause an increase of the gas flow shear on their surface. As a consequence, the agglomerate size is expected to decrease, which can explain the observed behavior. A model based on the balance between attractive and flow shear forces is presented that accounts for agglomerate size reduction as the strength of the field is increased.

Recent experiments have shown that a type of triaxial magnetic field we call a vortex field can induce strong mixing in a magnetic particle suspension. A vortex triaxial field consists of a rotating magnetic field in a horizontal plane, with a dc field applied normal to this. The mixing torque is found to be independent of the field frequency and fluid viscosity over a broad range; scales as the square of the applied field; and is strongest for a balanced triaxial field—one in which the root-mean-square amplitudes of the three field components are equal. In this paper we show that these anomalous effects are consistent with the formation of volatile particle chains that have a precessionlike motion. Theoretical results are given for both particle chains and magnetic rods for arbitrary vortex field angles. A key conclusion is that the mixing torque is independent of particle size, making this mixing technique scale adaptive, and thus suitable for microfluidics applications.

A simple homodimeric nanowalker is presented that is capable of moving processively along an extended periodic track. The unidirectional motion is based on a mechanism that makes use of the interaction between the two monomers and the thermal noise. The effect of the neck linker, which plays a critical role in the previously proposed design, plays an unimportant role in the present system. Except the requirement of a fixed binding orientation of the monomer relative to the track at the minimum of the potential well, the system has no other requirement for the form of the interaction potential between the motor and the track, which is critical to the unidirectional movement of the monomeric motor. Using detailed analyses and numerical simulations, it is shown that the homodimeric nanowalker walks hand over hand along the track with a high efficiency and a high stall force.

An exact analysis using the Langevin equation approach proves that an asymmetric-inhomogeneous harmonic chain with self-consistent inner reservoirs does not rectify heat, while it may show diffusive heat transport properties. Thus, we argue that the onset of a formal Fourier’s law in an asymmetric system does not guarantee an asymmetric heat flow.

The Kuramoto phase-diffusion equation is a nonlinear partial differential equation which describes the spatiotemporal evolution of a phase variable in an oscillatory reaction-diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in the form of dispersion leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second-order perturbation terms. We apply the theory to simple topologies, like a line or sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter, the synchronized state may become quasidegenerate. We demonstrate how perturbation theory fails at such a critical point.