Coexistence of distinct nonuniform nonequilibrium steady states in Ehrenfest multiurn model on a ring.

The recently proposed Ehrenfest M-urn model with interactions on a ring is considered as a paradigm model which can exhibit a variety of distinct nonequilibrium steady states. Unlike the previous three-urn model on a ring which consists of a uniform steady state and a nonuniform nonequilibrium steady state, it is found that for even M≥4, an additional nonequilibrium steady state can coexist with the original ones. Detailed analysis reveals that this additional nonequilibrium steady state emerged via a pitchfork bifurcation which cannot occur if M is odd. Properties of this nonequilibrium steady state, such as stability, and steady-state flux are derived analytically for the four-urn case. The full phase diagram with the phase boundaries is also derived explicitly. The associated thermodynamic stability is also analyzed, confirming its stability. These theoretical results are also explicitly verified by direct Monte Carlo simulations for the three-urn and four-urn ring models.

Theory of nonequilibrium asymptotic state thermodynamics: Interacting Ehrenfest urn ring as an example.

A generalized class of the nonequilibrium state, called the nonequilibrium asymptotic state (NEAS), is proposed. The NEAS is constructed within the framework of Fokker-Planck equations in thermodynamic limit. Besides the usual equilibrium state and nonequilibrium steady state (NESS), the class of NEAS could also cover the nonequilibrium periodic state (NEPS) in which its dynamics shows periodicity, the nonequilibrium quasiperiodic state (NEQPS), and nonequilibrium chaotic state (NECS) in which its dynamics becomes chaotic. Based on the theory of NEAS thermodynamics, the corresponding thermodynamics of different NEASs could also be determined. Finally the interacting Ehrenfest urn ring model is used as an example to illustrate how different kinds of NEAS (equilibrium state, uniform NESS, nonuniform NESS, NEPS) in the three-urn case are identified in our framework. In particular, the thermodynamics of NEPS and its phase transitions to other types of NEAS are studied.

Efficient reconstruction of directed networks from noisy dynamics using stochastic force inference.

We consider coupled network dynamics under uncorrelated noises that fluctuate about the noise-free long-time asymptotic state. Our goal is to reconstruct the directed network only from the time-series data of the dynamics of the nodes. By using the stochastic force inference method with a simple natural choice of linear polynomial basis, we derive a reconstruction scheme of the connection weights and the noise strength of each node. Explicit simulations for directed and undirected random networks with various node dynamics are carried out to demonstrate the good accuracy and high efficiency of the reconstruction scheme. We further consider the case when only a subset of the network and its node dynamics can be observed, and it is demonstrated that the directed weighted connections among the observed nodes can be easily and faithfully reconstructed. In addition, we propose a scheme to infer the number of hidden nodes and their effects on each observed node. The accuracy of these results is illustrated by simulations.

H-Theorem in an Isolated Quantum Harmonic Oscillator.

We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.

Phase transitions in Ehrenfest urn model with interactions: Coexistence of uniform and nonuniform states.

A model based on the classic noninteracting Ehrenfest urn model with two urns is generalized to M urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of nonuniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and nonuniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.

Ehrenfest urn model with interaction.

We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first- or second-order phase transition. The relaxation time to the equilibrium state, the Poincaré cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior the Poincaré cycles could serve as an indication to the nature of phase transition, and the behavior of the ratio of duration time of the states could be strong evidence of the metastability during first-order phase transition.

Development of melamine certified reference material in milk using two different isotope dilution mass spectrometry techniques.

A new certified reference material (CRM) of melamine in milk GLHK-11-02 was developed aiming to address the great demand from the testing community after the melamine crises. The material was prepared by adding an appropriate quantity of melamine into the skimmed milk samples and the final product was in the form of fine lyophilized powder. Characterization of the material relied on two newly developed gravimetric isotope dilution mass spectrometry (IDMS) methods, one using liquid chromatography-tandem mass spectrometry (LC-MS/MS) and another gas chromatography-mass spectrometry (GC-MS). Experimental parameters with crucial effects on the performance of the two IDMS methods were thoroughly investigated. These included purity of standard used, equilibration time of isotopes, efficiency of extraction methods as well as possible interferences from the matrix and melamine analogues. Precision was found to be excellent with a coefficient of variation of 2.5% for the LC-IDMS/MS (n=46) and 1.9% for the GC-IDMS (n=30) respectively. Using one-tail Student's t-test at 95% confidence interval, analytical data sets generated from the two methods were found to exhibit no significant difference. Measurement accuracy of the methods was further verified through an Asia Pacific Metrology Program (APMP) pilot study. Analytical results of the present LC-IDMS/MS for the two milk test samples at the concentration level of about 0.45 and 3.5 mg kg(-1) were proven to be very good. There were excellent overlaps between our results and the assigned reference values, and the absolute deviation was less than 3.2%. Both the LC-IDMS/MS and GC-IDMS methods were shown to be sufficiently reliable and accurate for certification of the melamine CRM. Certified value of melamine in dry mass fraction in GLHK-11-02 was 1.14 mg kg(-1). Expanded uncertainty due to sample inhomogeneity, long term and short term stability and variability in the characterization procedure was at 7.1% or 0.08 mg kg(-1). The CRM is primarily used to provide a complete method validation for and to improve the technical competence of melamine analysis to food and chemical testing laboratories.

Boundary condition of polyelectrolyte adsorption.

The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.

Anisotropic Fermi superfluid via p-wave Feshbach resonance.

We investigate theoretically fermionic superfluidity induced by Feshbach resonance in the orbital p-wave channel and determine the general phase diagram. In contrast with superfluid (3)He, due to the dipole interaction, the pairing is extremely anisotropic. When this dipole interaction is relatively strong, the pairing has symmetry k(z). When it is relatively weak, it is of symmetry k(z) + ibetak(y) (up to a rotation about z;, here beta < 1). A phase transition between these two states can occur under a change in the magnetic field or the density of the gas.

Conformational properties of an adsorbed charged polymer.

The behavior of a strongly charged polymer adsorbed on an oppositely charged surface of a low-dielectric constant is formulated by the functional integral method. By separating the translational, conformational, and fluctuational degrees of freedom, the scaling behaviors for both the height of the polymer and the thickness of the diffusion layer are determined. Unlike the results predicted by scaling theory, we identified the continuous crossover from the weak compression to the compression regime. All the analytical results are found to be consistent with Monte Carlo simulations. Finally, an alternative (operational) definition of a charged polymer adsorption is proposed.

Scaling theory of polyelectrolyte adsorption on a repulsive charged surface.

We studied the problem of many-polyelectrolyte adsorption on a repulsive charged surface by scaling analysis. According to ratio of the dielectric constant between the medium and the substrate, the phase diagrams of the adsorbed layer are divided into two classes. Their phase diagrams are qualitatively different. The polyelectrolytes of low (high) f Z2 are adsorbed for low (high) dielectric ratio, where f is the fraction of charged monomers and Z is the polyelectrolyte valency.

Adsorption transition of a polyelectrolyte on a high-dielectric charged substrate.

The behavior of a polyelectrolyte adsorbed on a charged surface of high-dielectric constant is studied by both Monte Carlo simulation and analytical methods. It is found that in a low ionic strength medium, the transition is first-order with the repulsive charged surface. The surface monomer density, which is the order parameter of the adsorption transition, follows a linear relation with surface charge density. It indicates that the polyelectrolyte is compressed on the substrate without any conformational change before the desorption. Finally, a different scaling law for the layer thickness is derived and verified by simulation.