Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

Pattern formation by growing droplets: The touch-and-stop model of growth

We investigate a novel model of pattern formation phenomena. In this model spherical droplets are nucleated on a substrate and grow at constant velocity; when two droplets touch each other they stop their growth. We examine the heterogeneous process in which the droplet formation is initiated on randomly distributed centers of nucleation and the homogeneous process in which droplets are nucleated spontaneously at constant rate. For the former process, we find that in arbitrary dimensiond the system reaches a jamming state where further growth becomes impossible. For the latter process, we observe the appearance of fractal structures. We develop mean-field theories that predict that the fraction of uncovered material (t) approaches to the jamming limit as (t)–()exp(Ct ^d ) for the heterogeneous process and as a power law for the homogeneous process. Exact solutions in one dimension are obtained and numerical simulations ford=1–3 are performed and compared with mean-field predictions.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

This paper shows the Fokker--Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker--Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time \tau and coloured cross-correlation strength \la.     

非高斯噪声驱动的双奇异随机系统的熵流与熵产生

研究了一类受非高斯噪声驱动的双奇异随机系统,应用路径积分法和变换的方法得到了该系统对应的Fokker-Plank方程,并结合Shannon信息熵的定义给出了此类系统的熵流与熵产生随时间演化的表达式,分析了非平衡约束下所引入的系统耗散参数、奇异性强度参数、噪声相关时间和噪声偏离参数对熵流与熵产生的影响. 关键词： 信息熵 熵流与熵产生 非高斯噪声 双奇异随机系统     

The computational complexity of pattern formation

The computational complexity of diffusion-limited aggregation and fluid invasion in porous media is studied. The time requirements on an idealized parallel computer for simulating the patterns formed by these models are investigated. It is shown that these growth models are P-complete. These results provide strong evidence that such pattern formation processes are inherently sequential and cannot be simulated efficiently in parallel.     

Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

We use an estimator of quantum criticality based on the entanglement entropy to discuss the ground state properties of the 1D anisotropic Kondo necklace model. We found that the T=0$T=0$ phase diagram of the model is described by a critical line separating an antiferromagnetic phase from a Kondo singlet state. Moreover we calculate the conformal anomaly on the critical line and obtain that c tends to 0.5 as the thermodynamic limit is reached. Hence we conclude that these transitions belong to Ising universality class being, therefore, second order transitions instead of infinite order as claimed before.     

色噪声驱动的双奇异随机系统的熵流与熵产生

讨论一类 (非平衡约束下) 高斯色噪声驱动的双奇异随机系统对应的Fokker-Planck方程，结合Shannon信息熵定义给出此类系统的熵流、熵产生随时间演化的精确表达式.分析(非平衡约束下)所引入的奇异性强度参数、噪声相关时间与耗散参数的相互作用以及对熵流、熵产生的显著影响. 关键词： 信息熵 熵流与熵产生 双奇异随机系统 高斯色噪声     

Entropy production in a cell and reversal of entropy flow as an anticancer therapy

The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and lowintensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently reverse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the biological tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful information from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.      

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Irreversibility and entropy production in transport phenomena,III—Principle of minimum integrated entropy production including nonlinear responses

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager–Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented.     

From lag synchronization to pattern formation in networked dynamics

The relationship between lag synchronization and pattern formation is investigated in this article by taking networked dynamics as spatio–temporal models. Firstly some results in two-dimensional open flow models with unidirectional coupling term are presented, and sufficient conditions for globally asymptotically stable lag synchronization in discrete and continuous cases are revealed by analytic method to elucidate the wave pattern evoked by the lag synchronization in such models. Then, an ad hoc network topology, a so-called “tier-network”, is introduced, which is an acyclic digraph with one center node and all the directed pathways from any other node to the center node are equal in length. And the dynamics in tier-networks is investigated. Some similarly sufficient conditions for globally asymptotically stable lag synchronization is obtained by analytic method, and the wave pattern in tier-networks evoked by lag synchronization is illustrated. The above results are supported by the numerical simulation in discrete case.     

Measure of irreversibility and entropy production in open quantum systems

A new concept of a measure of irreversibility for quantum dynamics in open systems is introduced as a suitably regularized substitute for the common notion of entropy production, which, unfortunately, yields infinite values for so many irreversible processes of physical relevance.     

Control of pattern formation by time-delay feedback with global and local contributions

We consider the suppression of spatiotemporal chaos in the complex Ginzburg-Landau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations.     

Onicescu information energy in terms of Shannon entropy and Fisher information densities

Following recent studies concerning the use of information theory in electronic structure theory of atomic and molecular systems, an analytical relationship between Onicescu information energy and densities of Shannon entropy and the two forms of the Fisher information has been presented. The established proof must be viewed in the light of the exponentially decaying nature of the asymptotic density of atoms and molecules.     

On the entropy production for the Davies model of heat conduction

The formula for the entropy production in open quantum systems is examined for the Davies model of heat conduction.This work is supported by Polish Ministry of Higher Education Science and Technology, project MRI 7.     

强迫耗散系统的有序结构和系统的发展(Ⅰ)，最小熵产生原理和有序结构

一个系统的发展总是由不可逆热力过程和非线性动力过程所驱动.将大气动力学方程组同考虑了动能变化的Gibbs关系结合起来构建的熵平衡方程，才能更好地描述大气系统的不可逆热力过程和非线性动力过程.至今非平衡态热力学仅利用Onsager线性唯象关系证明了最小熵产生原理.利用新建立的熵平衡方程和大气动力学方程的性质证明，最小熵产生原理在热力学线性区和非线性区都是普遍成立的.且当热量输送平衡、水汽输送平衡和动量输送平衡时，系统达到不可逆过程最弱的最小熵产生热力学状态.当系统又是动力平衡且无平流时，这种最小熵产生态就是 关键词： 非线性热力学 熵产生 最小熵产生原理 有序结构     

Hurst-Kolmogorov dynamics as a result of extremal entropy production

It is demonstrated that extremization of entropy production of stochastic representations of natural systems, performed at asymptotic times (zero or infinity) results in constant derivative of entropy in logarithmic time and, in turn, in Hurst-Kolmogorov processes. The constraints used include preservation of the mean, variance and lag-1 autocovariance at the observation time step, and an inequality relationship between conditional and unconditional entropy production, which is necessary to enable physical consistency. An example with real world data illustrates the plausibility of the findings.     

Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.     

The role of hydrophobic interaction in phase transition and structure formation of lipid membranes and proteins

The hydrophobic interaction arises from the ordered structure of water around nonpolar groups of molecules in an aqueous solvent. Because biological systems are made of various macromolecules and amphiphiles which are suspended in aqueous solution, the hydrophobic interaction plays a very important role in the formation of higher-order structure and phase transitions in biological systems. Considering the hydrophobic interaction, the van der Waals interaction and the entropic effect, an equation of state of a lipid membrane was obtained which was analogous to the van der Waals equation. The characteristics of the lipid bilayer phase transition as well as the phase behaviors of a lipid monolayer were explained by this equation of state. Experimental evidence was obtained from ultrasonic measurements which indicated that its phase transition accompanys significant critical phenomena. Analysis of the hydrophobicity of amino acid sequences revealed that the morphology of the proteins was determined by the hydrophobicity alone. The essential role of the hydrophobic interaction in the morphogenesis of proteins could be confirmed by a denaturation experiment on a soluble protein, carbonic anhydrase B. Fluorescence measurements showed that an intermediate state, the so-called molten globule state, had a quite hydrophobic core, indicating that the globule shape of this protein is stabilized by the hydrophobic interaction.