Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Nonequilibrium phase transition in the kinetic Ising model: Divergences of fluctuations and responses near the transition point

The nonequilibrium dynamic phase transition in the kinetic Ising model in the presence of an oscillating magnetic field is studied by Monte Carlo simulation. The fluctuation of the dynamic older parameter is studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined ''susceptibility'' is also studied near the dynamic transition point. Similarly, the fluctuation of energy and appropriately defined ''specific heat'' is studied as a function of temperature near the dynamic transition point. In both cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (in power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).

Nonequilibrium arrhythmic states and transitions in a mathematical model for diffuse fibrosis in human cardiac tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to N-f fibroblasts via a gap-junctional conductance G(gap), reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage P-f of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

A model for growth and engulfment of gas microporosity during aluminum alloy solidification process

A new coupled approach is presented for modeling the hydrogen bubble evolution and engulfment during an aluminum alloy solidification process in a micro-scale domain. An explicit enthalpy scheme is used to model the solidification process which is coupled with a level-set method for tracking the hydrogen bubble evolution. The volume averaging techniques are used to model mass, momentum, energy and species conservation equations in the chosen micro-scale domain. The interaction between the solid, liquid and gas interfaces in the system have been studied. Using an order-of-magnitude study on growth rates of bubble and solid interfaces, a criterion is developed to predict bubble elongation which can occur during the engulfment phase. Using this model, we provide further evidence in support of a conceptual thought experiment reported in literature, with regard to estimation of final pore shape as a function of typical casting cooling rates. The results from the proposed model are qualitatively compared with in situ experimental observations reported in literature. The ability of the model to predict growth and movement of a hydrogen bubble and its subsequent engulfment by a solidifying front has been demonstrated for varying average cooling rates encountered in typical sand, permanent mold, and various casting processes. (C) 2012 Elsevier B.V. All rights reserved.

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential.

An equivalent undercooling model to account for flow effect on binary alloy dendrite growth rate

A theoretical analysis is carried out to observe the influence of important flow parameters such as Nusselt number and Sherwood number on the tip speed of an equiaxed dendrite growing in a convecting alloy melt. The effect of thermal and solutal transfer at the interface due to convection is equated to an undercooling of the melt, and an expression is derived for this equivalent undercooling in terms of the flow Nusselt number and Sherwood number. Results for the equivalent undercooling are compared with corresponding numerical values obtained by performing simulations based on the enthalpy method. This method represents a relatively simple procedure to analyze the effects of melt convection on the growth rate of dendrites. (C) 2013 Elsevier Ltd. All rights reserved.

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential. (C) 2013 AIP Publishing LLC.

An enthalpy-based model of dendritic growth in a convecting binary alloy melt

Purpose-In the present work, a numerical method, based on the well established enthalpy technique, is developed to simulate the growth of binary alloy equiaxed dendrites in presence of melt convection. The paper aims to discuss these issues. Design/methodology/approach-The principle of volume-averaging is used to formulate the governing equations (mass, momentum, energy and species conservation) which are solved using a coupled explicit-implicit method. The velocity and pressure fields are obtained using a fully implicit finite volume approach whereas the energy and species conservation equations are solved explicitly to obtain the enthalpy and solute concentration fields. As a model problem, simulation of the growth of a single crystal in a two-dimensional cavity filled with an undercooled melt is performed. Findings-Comparison of the simulation results with available solutions obtained using level set method and the phase field method shows good agreement. The effects of melt flow on dendrite growth rate and solute distribution along the solid-liquid interface are studied. A faster growth rate of the upstream dendrite arm in case of binary alloys is observed, which can be attributed to the enhanced heat transfer due to convection as well as lower solute pile-up at the solid-liquid interface. Subsequently, the influence of thermal and solutal Peclet number and undercooling on the dendrite tip velocity is investigated. Originality/value-As the present enthalpy based microscopic solidification model with melt convection is based on a framework similar to popularly used enthalpy models at the macroscopic scale, it lays the foundation to develop effective multiscale solidification.

An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

Effect of shrinkage induced flow on binary alloy dendrite growth: An equivalent undercooling model

This paper presents a theoretical model for studying the effects of shrinkage induced flow on the growth rate of binary alloy dendrites. An equivalent undercooling of the melt is defined in terms of ratio of the phase densities to represent the change in dendrite growth rate due to variation in solutal and thermal transport resulting from shrinkage induced flow. Subsequently, results for dendrite growth rate predicted by the equivalent undercooling model is compared with the corresponding predictions obtained using an enthalpy based numerical method for dendrite growth with shrinkage. The agreement is found to be good. Published by Elsevier Ltd.

Inhibition of p300 lysine acetyltransferase activity by luteolin reduces tumor growth in head and neck squamous cell carcinoma (HNSCC) xenograft mouse model

Chromatin acetylation is attributed with distinct functional relevance with respect to gene expression in normal and diseased conditions thereby leading to a topical interest in the concept of epigenetic modulators and therapy. We report here the identification and characterization of the acetylation inhibitory potential of an important dietary flavonoid, luteolin. Luteolin was found to inhibit p300 acetyltransferase with competitive binding to the acetyl CoA binding site. Luteolin treatment in a xenografted tumor model of head and neck squamous cell carcinoma (HNSCC), led to a dramatic reduction in tumor growth within 4 weeks corresponding to a decrease in histone acetylation. Cells treated with luteolin exhibit cell cycle arrest and decreased cell migration. Luteolin treatment led to an alteration in gene expression and miRNA profile including up-regulation of p53 induced miR-195/215, let7C; potentially translating into a tumor suppressor function. It also led to down regulation of oncomiRNAs such as miR-135a, thereby reflecting global changes in the microRNA network. Furthermore, a direct correlation between the inhibition of histone acetylation and gene expression was established using chromatin immunoprecipitation on promoters of differentially expressed genes. A network of dysregulated genes and miRNAs was mapped along with the gene ontology categories, and the effects of luteolin were observed to be potentially at multiple levels: at the level of gene expression, miRNA expression and miRNA processing.

Novel derivatives of spirohydantoin induce growth inhibition followed by apoptosis in leukemia cells

Hydantoin derivatives possess a variety of biochemical and pharmacological properties and consequently are used to treat many human diseases. However, there are only few studies focusing on their potential as cancer therapeutic agents. In the present study, we have examined anticancer properties of two novel spirohydantoin compounds, 8-(3,4-difluorobenzyl)-1'-(pent-4-enyl)-8-azaspiro[bicyclo[3.2.1] octane-3,4'-imidazolidine]-2',5'-dione (DFH) and 8-(3,4-dichlorobenzyl)-1'-(pent-4-enyl)-8-azaspiro[bicyclo[3.2.1]octane-3,4'-imidazolidine]-2',5'-dione (DCH). Both the compounds exhibited dose- and time-dependent cytotoxic effect on human leukemic cell lines, K562, Reh, CEM and 8ES. Incorporation of tritiated thymidine ([H-3) thymidine) in conjunction with cell cycle analysis suggested that DFH and DCH inhibited the growth of leukemic cells. Downregulation of PCNA and p-histone H3 further confirm that the growth inhibition could be at the level of DNA replication. Flow cytometric analysis indicated the accumulation of cells at subG1 phase suggesting induction of apoptosis, which was further confirmed and quantified both by fluorescence-activated cell sorting (FACS) and confocal microscopy following annexin V-FITC/propidium iodide (PI) staining. Mechanistically, our data support the induction of apoptosis by activation of the mitochondrial pathway. Results supporting such a model include, elevated levels of p53, and BAD, decreased level of BCL2, activation and cleavage of caspase 9, activation of procaspase 3, poly (ADP-ribosyl) polymerase (PARP) cleavage, downregulation of Ku70, Ku80 and DNA fragmentation. Based on these results we discuss the mechanism of apoptosis induced by DFH and its implications in leukemia therapy. (C) 2008 Elsevier Inc. All rights reserved.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Different phenomenological theories and their abilities to describe the interdiffusion process in a binary system during multiphase growth

There are essentially two different phenomenological models available to describe the interdiffusion process in binary systems in the olid state. The first of these, which is used more frequently, is based on the theory of flux partitioning. The second model, developed much more recently, uses the theory of dissociation and reaction. Although the theory of flux partitioning has been widely used, we found that this theory does not account for the mobility of both species and therefore is not suitable for use in most interdiffusion systems. We have first modified this theory to take into account the mobility of both species and then further extended it to develop relations or the integrated diffusion coefficient and the ratio of diffusivities of the species. The versatility of these two different models is examined in the Co-Si system with respect to different end-member compositions. From our analysis, we found that the applicability of the theory of flux partitioning is rather limited but the theory of dissociation and reaction can be used in any binary system.