A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.

The temperature increase of a thin water layer is investigated, both experimentally and numerically, when the layer is heated by an infrared laser. The laser is focused to a waist of $5.3\mu \mathrm{m}$ inside a $28\mu \mathrm{m}$ gap that contains fluorescent aqueous solutions between two glass slides. Temperature fields are measured using the temperature sensitivity of rhodamine-B, while correcting for thermal diffusion using rhodamine-101, which is insensitive to temperature. In the steady state, the shape of the hot region is well fitted with a Lorentzian function whose width ranges between 15 and $30\mu \mathrm{m}$, increasing with laser power. At the same time, the maximum temperature rise ranges between 10 and $55°\mathrm{C}$ and can display a decrease at high laser powers. The total energy stored in the sample increases linearly with the laser power. The dynamics of the heating occurs with two distinct time scales: (i) a fast time (${\tau }_{\Theta }=4.2\mathrm{ms}$ in our case) which is the time taken to reach the maximum temperature at the laser position and the maximum temperature gradient, and (ii) a slow time scale for the spatial profile to reach its final width. The temperature field obtained numerically agrees quantitatively with the experiments for low laser powers but overpredicts the temperature rise while underpredicting the profile width for high powers. The total energy shows good agreement between experiments and simulations for all laser powers, suggesting that the discrepancies are due to a broadening of the laser, possibly due to a thermal lensing effect.

The role of chirality in membrane-forming lipids is not well appreciated at present. Here we demonstrate that the chirality of phospholipids makes fluid lipid bilayers piezoelectric. Thus, chiral lipids would play a central role in the functioning of cell membranes as active mechanotransducers. By periodically shearing and compressing nonaqueous lamellar phases of left ($L\text{−}\alpha$-phosphatidylcholine), right (D-$\alpha$-phosphatidylcholine), and racemic (DL-$\alpha$-phosphatidylcholine) lipids, we induced a tilt of the molecules with respect to the bilayer’s normal and produced electric current perpendicular to the tilt plane, with the chiral lipids only. This effect is due to the $\mathrm{Sm}\text{−}{A}^{*}$ phase liquid crystal structure of the bilayers, which under molecular tilt becomes a ferroelectric $\mathrm{Sm}\text{−}{C}^{*}$ phase, where the polarization is normal to the tilt plane. This coupling allows for a wide variety of sensory possibilities of cell membranes such as mechanoreception, magnetosensitivity, as well as in-plane proton membrane transport and related phenomena such as adenosine triphosphate (ATP) synthesis, soft molecular machine performance, etc.

The impact of magnetic nanoparticles with different surface coating upon the isotropic-to-nematic and nematic-to-smectic-$A$ phase transitions of the liquid crystal octylcyanobiphenyl is explored by means of high-resolution adiabatic scanning calorimetry. A shrinkage of the nematic range is observed, which is strongly dependent on the surface coating of the nanoparticles. The isotropic-to-nematic transition remains weakly first order while the nematic-to-smectic-$A$ is continuous with the effective critical exponent $\alpha$ values (0.35 and 0.39, depending on the coating) between the pure octylcyanobiphenyl value of $0.31\pm 0.03$ and the theoretical tricritical value of 0.5.

Self-consistent evaluations of both the transmembrane potential (TMP) and possible electroporation density across membrane of spheroidal cells in response to ultrashort, high-intensity pulses are reported and discussed. Most treatments in the literature have been based on spherical cells, and this represents a step towards more realistic analyses. The present study couples the Laplace equation with Smoluchowski theory of pore formation, to yield dynamic membrane conductivities that influence the TMP. It is shown that the TMP induced by pulsed external voltages can be substantial higher in oblate spheroids as compared to spherical or prolate spheroidal cells. Flattening of the surface area in oblate spheroids leads to both higher electric fields seen by the membrane, and allows a great fraction of the surface area to be porated. This suggests that biomedical applications such as drug delivery and electrochemotherapy could work best for flatter-shaped cells, and secondary field-enabled orienting would be beneficial. Results for arbitrary field orientations and different cell sizes have also been presented.

Piéron’s law relates human reaction times to the intensity of a sensory stimulus by a power function. The neural processes responsible for this nonlinear behavior are not understood. A simple neural model based on the Brownian motion of spikes and information theory is presented. The model shows that Piéron’s law is a transformation function in time. The shape of Piéron’s law is invariant and scales into the intensity-response function of single neurons in a fractal-like process. The model also shows that Piéron’s law gives rise to $1∕f^{\alpha }$ noise together with a high-frequency thermal noise limit. It is proposed that the biophysical origin of reaction time variability is related to a form of noise-induced synchronization in weakly coupled neurons. The implications in visual-motor transduction are discussed.

The time dependence of the x-ray absorption of aluminum samples heated with intense radiation sources from a foam-buffered gold hohlraum has been studied in this work. Hydrodynamic simulations were used to illustrate the plasma conditions in the plastic-tamped aluminum foils contained in this type of hohlraum. Experiments were conducted to measure the $K$-shell x-ray absorption spectra of the aluminum sample. With densities taken from the hydrodynamic simulations, electron temperatures were then inferred by fitting the measured absorption spectra with detailed-term-accounting calculations. The inferred temperatures have a maximum of about $93\mathrm{eV}$ and were found to agree within 25% with the simulated results at times after $1\mathrm{ns}$, indicating that the use of foam shields, together with a compact cavity, has created a clean and high-temperature radiation source preferable to opacity measurements.

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential.

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

Athreya, Goldenfeld, and Dantzig [Phys. Rev. E 74, 011601 (2006)] claim that the current implementation of the renormalization-group method neglects the proper ordering of renormalization and differentiation. Their analysis is, however, based on the wrong multiple-scales method results.

In a recent Comment [Y. Shiwa, Phys. Rev. E 79, 013601 (2009)], Shiwa points out that our multiple-scales analysis of the Van der Pol equation [Appendix of Phys. Rev. E 74, 011601 (2006)] contained an error, and thus there may be no ordering ambiguity for renormalization and differentiation operations, as we had proposed for the phase-field crystal equation and other conservation laws. The Van der Pol analysis was indeed incorrect, and while his Comment casts doubt over our treatment of the multiple-scales analysis of the phase-field crystal (PFC) equation, there is no substantial change to our renormalization (RG) group results or simulations of the PFC model. This example highlights the merits of the RG approach to singular perturbation problems: the RG method is more mechanical and requires less user-insight than traditional methods.

A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.

We study Brownian motion driven with both conservative and nonconservative external forces. By using the thermodynamic approach of the theory of Brownian motion we obtain the Fokker-Planck equation and derive expressions for the fluctuation theorem in local equilibrium and in quasiequilibrium. In local equilibrium the expressions we obtain coincide with previous results.

It has recently been found in some dynamical systems in fluid dynamics that only a few unstable periodic orbits (UPOs) with low periods can give good approximations to the mean properties of turbulent (chaotic) solutions. By employing three chaotic systems described by ordinary differential equations, we compare time-averaged properties of a set of UPOs and those of a set of segments of chaotic orbits. For every chaotic system we study, the distributions of a time average of a dynamical variable along UPOs with lower and higher periods are similar to each other and the variance of the distribution is small, in contrast with that along chaotic segments. The distribution seems to converge to some limiting distribution with nonzero variance as the period of the UPO increases, although that along chaotic orbits inclines to converge to a $\delta$-like distribution. These properties seem to lie in the background of why only a few UPOs with low periods can give good mean statistical properties in dynamical systems in fluid dynamics.

The branching aftershock sequence (BASS) model is a self-similar statistical model for earthquake aftershock sequences. A prescribed parent earthquake generates a first generation of daughter aftershocks. The magnitudes and times of occurrence of the daughters are obtained from statistical distributions. The first generation daughter aftershocks then become parent earthquakes that generate second generation aftershocks. The process is then extended to higher generations. The key parameter in the BASS model is the magnitude difference $\Delta m^{*}$ between the parent earthquake and the largest expected daughter earthquake. In the application of the BASS model to aftershocks $\Delta m^{*}$ is positive, the largest expected daughter event is smaller than the parent, and the sequence of events (aftershocks) usually dies out, but an exponential growth in the number of events with time is also possible. In this paper we explore this behavior of the BASS model as $\Delta m^{*}$ varies, including when $\Delta m^{*}$ is negative and the largest expected daughter event is larger than the parent. The applications of this self-similar branching process to biology and other fields are discussed.

The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH equation has been recently extended to a two-component integrable system (CH2), which includes both velocity and density variables in the dynamics. Although possessing peakon solutions in the velocity, the CH2 equation does not admit singular solutions in the density profile. We modify the CH2 system to allow a dependence on the average density as well as the pointwise density. The modified CH2 system (MCH2) does admit peakon solutions in the velocity and average density. We analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially confined initial data. Numerical results for the MCH2 system are given and compared with the pure CH2 case. These numerics show that the modification in the MCH2 system to introduce the average density has little short-time effect on the emergent dynamical properties. However, an analytical and numerical study of pairwise peakon interactions for the MCH2 system shows a different asymptotic feature. Namely, besides the expected soliton scattering behavior seen in overtaking and head-on peakon collisions, the MCH2 system also allows the phase shift of the peakon collision to diverge in certain parameter regimes.

The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking nonmonotonic dependence of the long-time self-diffusion on the concentration of DNA in low-salt conditions. This generic nonmonotonic behavior results from the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.

We address the question of the effect of disorder on heat conduction in an anharmonic chain with interactions given by the Fermi-Pasta-Ulam (FPU) potential. In contrast to the conclusions of an earlier paper [Phys. Rev. Lett. 86, 63 (2001)], which found that disorder could induce a finite thermal conductivity at low temperatures, we find no evidence of a finite-temperature transition in conducting properties. Instead, we find that at low temperatures, small system-size transport properties are dominated by disorder but the asymptotic system size dependence of current is given by the usual FPU result $J\sim 1∕N^{2∕3}$. We also present interesting results on the binary-mass ordered FPU chain.

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway’s model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.