The parameter conversion from the Kedem-Katchalsky model into the two-parameter model

Cryopreservation is an important process for preserving cells and tissues. The process itself can, however, cause damage to cells and tissues. During addition and removal of a cryoprotective agent (CPA), cells are subjected to imbalanced osmotic pressures between the intracellular and extracellular solutions. Cells can be injured if these shrinkage and swelling events are beyond their tolerable limits. The characteristics of the cell volume changes during these processes depend on the types of CPA, the methods of adding and removing of the CPA and the permeability of cells to CPA and water. The typical models of this transportation are the two-parameter (2-p) model and the Kedem-Katchalsky (K-K) model. The K-K model is more general than the 2-p model. However, there is evidence that in many cases water and CPAs do not permeate through common pathways, hence the use of the reflection coefficient in the K-K model may be unnecessary and in some cases it may create conceptual errors. Therefore, the 2-p model is more suitable for use as a transport model than the K-K model. The aim of this study is to use the values of the K-K model parameters from data in the literature to calculate the corresponding parameters for the 2-p model. The results from these simulations demonstrate that the cell volume changes during CPA addition and removal from the K-K model can be closely estimated by the 2-p model.     

On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability

In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.     

Application of the Englert-Schwinger model to the equation of state and the fullerene molecule

The Englert-Schwinger model (ESM) is applied to two problems. One is the calculation of zero-temperature equation of state (EOS) of elements within the spherically symmetric Wigner-Sietz cell approximation. The other is to obtain the equilibrium radius of fullerene molecule using March’s approach [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. In each case, the results of the ESM are compared with those of Thomas-Fermi-Dirac (TFD) and Thomas-Fermi-Dirac-Weizsacker (TFDW) models. Zero-temperature equation of state calculations are done for Al and Cu. The results of the ESM show an enormous improvement over those of the TFD model. Also, the ESM is in good agreement with the TFDW model for compressions greater than 2. In the regime of validity of TFDW theory, i.e., compressions greater than 20 and 10 for Al and Cu, respectively, the deviations between the results of the two models are negligible. Hence, the ESM may be used in lieu of the TFDW model for EOS calculations. In the fullerene case, we have obtained the cohesive energy using the models assuming the radius obtained from accurate calculations of the fullerene molecule. We have also obtained the equilibrium radius predicted by each model. The results obtained show that the ESM results are not much of an improvement over the TFD results. This shows that the ESM cannot always improve the results of the TFD model and be a replacement for the TFDW model. However, as in the EOS case, it would give results in good agreement with TFDW results for properties that are dependent on the electron density at the outer reaches of the atom.     

Application of the SCC method to the multi-O(4) model: The collective Hamiltonian

The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the sp...     

Fractal Aggregation Near the Threshold

In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P_ca=0.69±0.02 for model 1 and P_ca=0.72±0.01 for model 2, critical fractal dimension. D_c= 1.71±0.06 for model 1 and D_c=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.     

Universality classes in the random-storage sandpile model

The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with a deterministic toppling rule. Based on the moment analysis of the distribution of avalanche sizes we conclude that for 0相似文献   

On the structure of the nucleon optical potential

A generalization of the exciton model for preequilibrium decay of the compound nucleus is presented. This model successfully describes both spectra and angular distributions of neutrons and protons emitted in reactions induced by light (A≦4) projectiles. Limitations of the model due to the finite nuclear geometry are discussed. The connection with a statistical model for the nuclear Hamiltonian is established.     

Evaluation of the void fraction in the crescent-shape moderator cell of the CARR-CNS

The mathematical model developed in a previous paper is improved in the present paper for analyzing and evaluating the void fraction profiles in the crescent-shape moderator cell of the Cold Neutron Source (CNS) of the China Advanced Research Reactor (CARR) which is now under construction in the China Institute of Atomic Energy (CIAE). The model is then applied to the case of the CARR-CNS with liquid hydrogen as a moderator and the void fraction in the crescent-shape moderator cell of the CARR-CNS is evaluated. The calculation results show that the void fraction in the crescent-shape moderator cell less than 20%. The model and the calculation results will help to obtain insight of the mechanism that controls the void fraction distribution in the crescent-shape moderator cell, and provide theoretical supports for the moderator cell construction.     

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Fröhlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Fröhlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.     

Modelling the spontaneous combustion of coal: the adiabatic testing procedure

A general approach is described for modelling problems that involve heat and mass transfer in coal, such as spontaneous combustion. It is based on the TOUGH2 code, which is a general-purpose simulator for modelling multi-component, multi-phase, non-isothermal flow in a porous medium. An equation of state (EOS) module for TOUGH2 is developed, which includes accurate physical properties for all of the gases involved (N₂, oxygen and carbon dioxide). The new simulator is then used to model the adiabatic method for testing the reactivity of coal samples. An important part of the model development is the selection of the approximate representation of the reaction of coal with oxygen. The results show that (i) using dual Arrhenius parameters and (ii) representing the heat-release as an oxidation reaction rather than a purely thermal reaction both significantly improve the match of the model to the experimental data.     

The effective hydrodynamic radius in the Stokes–Einstein relation is not a constant

Variants based on the assumption of effective hydrodynamic radius being a constant are usually adopted to test the Stokes–Einstein (SE) relation. The rationality of the assumption is examined by performing molecular dynamics simulations with the truncated Lennard-Jones-like (TLJ) model, Kob–Andersen model and ortho-terphenyl (OTP) model. The results indicate the assumption is generally not established except for special case. The effective hydrodynamic radius is observed to increase with decreasing temperature for TLJ model but is decreased for Kob–Andersen and OTP model; and which is almost a constant for TLJ particle with enough rigidity. The variant of SE relation $D\sim T/\eta $ is invalid for the three models except for the TLJ particle with enough rigidity. We propose similar inconsistency may be also existed in other liquids and the assumption should be critically evaluated when adopted to test the SE relation.     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.     

The existence of the t-quark and its relation to decays of the B mesons

We construct the general five quark model in SU(2) × U(1) and study its phenomenological consequences, in particular its predictions for B states. The model is consistent with experiments and we estimate semileptonic decays that distinguish it from the sequential model.     

Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface

A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model.     

Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.     

Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator for the convection–diffusion equation is presented. The model uses seven discrete velocities in three dimensions (D3Q7 model). The off-diagonal components of the relaxation-time matrix, which originate from the rotation of the principal axes, enable us to take into account full anisotropy of diffusion. An asymptotic analysis of the model equation with boundary rules for the Dirichlet and Neumann-type (specified flux) conditions is carried out to show that the model is first- and second-order accurate in time and space, respectively. The results of the analysis are verified by several numerical examples. It is also shown numerically that the error of the MRT model is less sensitive to the variation of the relaxation-time coefficients than that of the classical BGK model. In addition, an alternative treatment for the Neumann-type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary.     

Heat capacities of the dipolar Yukawa model polar fluid

The Stockmayer fluid is often used to describe a polar fluid. The dipolar Yukawa (DY) fluid is also a useful model for such fluids and is convenient for theoretical applications. Here we use the mean spherical approximation (MSA) and perturbation theory (PT) to study the heat capacities of the DY fluid model of a polar fluid and compare these results with Monte Carlo simulations for this model polar fluid. We find that the DY fluid shows the same features as the Stockmayer fluid does; demonstrating the utility of the DY fluid and further finding that the MSA and PT approaches give reasonably accurate results for the heat capacity.     

A practical second-order electromagnetic model in the quasi-specular regime based on the curvature of a 'good-conducting' scattering surface

This letter presents an approximate second-order electromagnetic model where polarization coefficients are surface dependent up to the curvature order in the quasi-specular regime. The scattering surface is considered 'good-conducting' as opposed to the case for our previous derivation where perfect conductivity was assumed. The model reproduces dynamically, depending on the properties of the scattering surface, the tangent-plane (Kirchhoff) or the first-order small-perturbation (Bragg) limits. The convergence is assumed to be ensured by the surface curvature alone. This second-order model is shown to be consistent with the small-slope approximation of Voronovich (SSA-1+SSA-2) for perfectly conducting surfaces. Our model differs from SSA-1 + SSA-2 in its dielectric expression, to correct for a full convergence toward the tangent-plane limit under the 'good-conducting' approximation. This new second-order formulation is simple because it involves a single integral over the scattering surface and therefore it is suitable for a vast array of analytical and numerical applications in quasi-specular applications.     

Exact solution of the multiflavor gross-neveu model

The Bethe-ansatz solution is presented for the multiflavor model arising in the Polyakov-Wiegmann fermionization of the SU(2) principal chiral field, i.e. the O(4) σ model. The vacuum and excitations with finite energy and momentum are constructed. The assumption that massive particles of the σ model are in the vector representation of O(4) is not corroborated. The renormalization-group β function agrees with a one-charge solution in perturbation theory.     

On the thermodynamics of the random one-dimensional Ising chain in a transverse field

For three simple one-dimensional disordered models: (a) the Ising chain with random magnetic moments in a transverse field, (b) the Ising chain with random coupling constants in a transverse field, and (c) the X-Y model with a special type of disorder, the asymptotic equivalence in the thermodynamic limit is proved and some of its consequences are discussed. The spectral density of the finite chain for the model (a) is calculated by Dean's method for several representative cases and the presence of the local modes is indicated. The expressions for the initial susceptibilities for the models (a) and (b) are reviewed and (in two cases) the derivations are simplified.