A class of irrotational, isentropic, and compressible flows is studied theoretically by formulating the density and the velocity potential in a Madelung transformation. The resulting nonlinear Schrödinger equation is solved in terms of similarity variables. One particular family of exact solutions, valid for any ratio of the specific heat capacities of the gas, permits explicit expressions of the fluid properties and velocities in terms of time and spatial coordinates. Analytically, the density is a Gaussian function of the similarity variable, while the temperature is a function of time only. This method is applicable in one (1D), two, and three dimensional geometries. As a simple example, a 1D gas column, with mass injection on one side and a steadily translating wall on the other, can be formulated exactly. The connection with the evolution of an unsteady velocity potential will also be examined.

The formation of a transient internal transport barrier (ITB) is observed after the electron-cyclotron-resonance-heating (ECRH) switch-off in the HL-2A plasmas, characterized by transient increase of central electron temperature. The newly developed correlation reflectometer provided direct measurements showing reduction of turbulence in the region of steepened gradients for the period of ITB formation triggered by the ECRH switch-off. Furthermore, the reduction of core turbulence is correlated in time with the appearance of a low-frequency mode with a spectrally broad poloidal structure that peaks near zero frequency in the core region. These structures have low poloidal mode number, high poloidal correlation, and short radial correlation and are strongly coupled with high-frequency ambient turbulence. Observation indicates that these structures play important roles in the reduction of the core turbulence and in improvements of the core transport after the off-axis ECRH is turned off.

The macroscopic conservation equations of radiation energy and radiation momentum are derived on the basis of radiation hydrodynamics. Based on the Chapman-Enskog method, the lattice Boltzmann model for one-dimensional radiative transfer is proposed from the Boltzmann equation. The numerical simulation results agree well with the exact solution and show that the lattice Boltzmann method developed in this paper has good accuracy and stability for solving one-dimensional radiative transfer problems.

We study the nature of workplace stress from the aspect of human-human interactions. We investigated the distribution of Center for Epidemiological Studies Depression Scale scores, a measure of the degree of stress, in workplaces. We found that the degree of stress people experience when around other highly stressed people tends to be low, and vice versa. A simulation based on a model describing microlevel human-human interaction reproduced this observed phenomena and revealed that the energy state of a face-to-face communication network correlates with workplace stress macroscopically.

We address a central issue of phononics: the search of properties or mechanisms to manage the heat flow in reliable materials. We analytically study standard and simple systems modeling the heat flow in solids, namely, the harmonic, self-consistent harmonic and also anharmonic chains of oscillators, and we show an interesting insulating effect: While in the homogeneous models the heat flow decays as the inverse of the particle mass, in the chain with alternate masses it decays as the inverse of the square of the mass difference, that is, it decays essentially as the mass ratio (between the smaller and the larger one) for a large mass difference. A similar effect holds if we alternate on-site potentials instead of particle masses. The existence of such behavior in these different systems, including anharmonic models, indicates that it is a ubiquitous phenomenon with applications in the heat flow control.

We present an experimental study of disordered packings of deformable spheres. Fluorescent hydrogel spheres immersed in water together with a tomography technique enabled the imaging of the three-dimensional arrangement. The mechanical behavior of single spheres subjected to compression is first examined. Then the properties of packings of a randomized collection of deformable spheres in a box with a moving lid are tested. The transition to a state where the packing withstands finite stresses before yielding is observed. Starting from random packed states, the power law dependence of the normal force versus packing fraction or strain at different velocities is quantified. Furthermore, a compression-decompression sequence at low velocities resulted in rearrangements of the spheres. At larger packing fractions, a saturation of the mean coordination number took place, indicating the deformation and faceting of the spheres.

In the present study we investigate computationally the steady-state motion of an elastic capsule along the centerline of a square microfluidic channel and compare it with that in a cylindrical tube. In particular, we consider a slightly over-inflated elastic capsule made of a strain-hardening membrane with comparable shearing and area-dilatation resistance. Under the conditions studied in this paper (i.e., small, moderate, and large capsules at low and moderate flow rates), the capsule motion in a square channel is similar to and thus governed by the same scaling laws with the capsule motion in a cylindrical tube, even though in the channel the cross section in the upstream portion of large capsules is nonaxisymmetric (i.e., square-like with rounded corners). When the hydrodynamic forces on the membrane increase, the capsule develops a pointed downstream edge and a flattened rear (possibly with a negative curvature) so that the restoring tension forces are increased as also happens with droplets. Membrane tensions increase significantly with the capsule size while the area near the downstream tip is the most probable to rupture when a capsule flows in a microchannel. Because the membrane tensions increase with the interfacial deformation, a suitable Landau-Levich-Derjaguin-Bretherton analysis reveals that the lubrication film thickness $h$ for large capsules depends on both the capillary number Ca and the capsule size $a$; our computations determine the latter dependence to be (in dimensionless form) $h\sim a^{-2}$ for the large capsules studied in this work. For small and moderate capsule sizes $a$, the capsule velocity $U_x$ and additional pressure drop $\Delta P^{+}$ are governed by the same scaling laws as for high-viscosity droplets. The velocity and additional pressure drop of large thick capsules also follow the dynamics of high-viscosity droplets, and are affected by the lubrication film thickness. The motion of our large thick capsules is characterized by a $U_x-\mathcal{U}\sim h\sim a^{-2}$ approach to the undisturbed average duct velocity and an additional pressure drop $\Delta P^{+}\sim a^3/h\sim a^5$. By combining basic physical principles and geometric properties, we develop a theoretical analysis that explains the power laws we found for large capsules.

A model is constructed to study the phenomenon of bursting in cultured neuronal networks by considering the effects of glial release and the extrasynaptic receptors on neurons. In the frequently observed situations of synchronized bursting, the whole neuronal network can be described by a mean-field model. In this model, the dynamics of the synchronized network in the presence of glia is represented by an effective two-compartment neuron with stimulations on both the dendrite and soma. Numerical simulations of this model show that most of the experimental observations in bursting, in particular the high plateau and the slow repolarization, can be reproduced. Our findings suggest that the effects of glia release and extrasynaptic receptors, which are usually neglected in neuronal models, can become important in intense network activities. Furthermore, simulations of the model are also performed for the case of glia-suppressed cultures to compare with recent experimental results.

We propose a framework for the spontaneous motion of a droplet coupled with internal dynamic patterns generated in a reaction-diffusion system. The spatiotemporal order of the chemical reaction gives rise to inhomogeneous surface tension and results in self-propulsion driven by the surrounding flow due to the Marangoni effect. Numerical calculations of internal patterns together with theoretical results of the flow fields at low Reynolds number reproduce well the experimental results obtained using a droplet of the Belousov-Zhabotinsky reaction medium.

We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system’s state. This allows us to directly study entropy production in systems with microscopic irreversibility. The two sampling methods are equivalent otherwise, and the fluctuation theorem also holds for the different paths. We focus on a fully irreversible three-state loop, as a canonical model of microscopic irreversibility, finding its entropy distribution, rate of entropy production, and large deviation function in closed analytical form, and showing that the observed kink in the large deviation function arises solely from microscopic irreversibility.

We study the buckling of a two-dimensional elastica floating on a bath of dense fluid, subjected to axial compression. The sinusoidal pattern predicted by the analysis of linear stability is shown to become localized above the buckling threshold. A nonlinear amplitude equation is derived for the envelope of the pattern. These results provide a simple interpretation to the wrinkle-to-fold transition reported by Pocivavsek et al. [Science 320, 912 (2008)]. An analogy with the classical problem of the localized buckling of a strut on a nonlinear elastic foundation is presented.

Blood viscosity is a major factor in heart disease. When blood viscosity increases, it damages blood vessels and increases the risk of heart attacks. Currently, the only method of treatment is to take drugs such as aspirin, which has, however, several unwanted side effects. Here we report our finding that blood viscosity can be reduced with magnetic fields of 1 T or above in the blood flow direction. One magnetic field pulse of 1.3 T lasting ∼1 min can reduce the blood viscosity by 20%-30%. After the exposure, in the absence of magnetic field, the blood viscosity slowly moves up, but takes a couple of hours to return to the original value. The process is repeatable. Reapplying the magnetic field reduces the blood viscosity again. By selecting the magnetic field strength and duration, we can keep the blood viscosity within the normal range. In addition, such viscosity reduction does not affect the red blood cells’ normal function. This technology has much potential for physical therapy.

In this paper, we completely solve the problem of the ground states of the lattice-gas model on the infinite plane triangular lattice with nearest- and next-nearest-neighbor pairwise interactions and with additional interaction between three particles at the vertices of a nearest-neighbor triangle. We use this model to illustrate how the complete solution of the ground-state problem of a lattice-gas model (or equivalent spin model) should look.

We consider a two-dimensional gas of colliding charged particles confined to finite size containers of various geometries and subjected to a uniform orthogonal magnetic field. The gas spectral densities are characterized by a broad peak at the cyclotron frequency. Unlike for infinitely extended gases, where the amplitude of the cyclotron peak grows linearly with temperature, here confinement causes such a peak to go through a maximum for an optimal temperature. In view of the fluctuation-dissipation theorem, the reported resonance effect has a direct counterpart in the electric susceptibility of the confined magnetized gas.

The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with an exact renormalization group and parallel-tempering Monte Carlo simulations. The grand canonical partition function of the equivalent hard-core repulsive lattice-gas problem is recast first as an Ising-like canonical partition function, which allows for a closed set of renormalization-group equations. The flow of these equations is analyzed for the limit of infinite chemical potential, at which the vertex-cover problem is attained. The relevant fixed point and its neighborhood are analyzed and nontrivial results are obtained both for the coverage as well as for the ground-state entropy density, which indicates the complex structure of the solution space. Using special hierarchy-dependent operators in the renormalization group and Monte Carlo simulations, structural details of optimal configurations are revealed. These studies indicate that the optimal coverages (or packings) are not related by a simple symmetry. Using a clustering analysis of the solutions obtained in the Monte Carlo simulations, a complex solution space structure is revealed for each system size. Nevertheless, in the thermodynamic limit, the solution landscape is dominated by one huge set of very similar solutions.

Geometric stochastic resonance of particles diffusing across a porous membrane subject to oscillating forces is characterized as a synchronization process. Noninteracting particle currents through a symmetric membrane pore are driven either perpendicular or parallel to the membrane, whereas, harmonic-mixing spectral current components are generated by the combined action of perpendicular and parallel drives. In view of potential applications to the transport of colloids and biological molecules through narrow pores, we also consider the role of particle repulsion as a controlling factor.