Application of Statistical Physics to Understand Static and Dynamic Anomalies in Liquid Water

We present an overview of recent research applying ideas of statistical mechanics to try to better understand the statics and especially the dynamic puzzles regarding liquid water. We discuss recent molecular dynamics simulations using the Mahoney–Jorgensen transferable intermolecular potential with five points (TIP5P), which is closer to real water than previously-proposed classical pairwise additive potentials. Simulations of the TIP5P model for a wide range of deeply supercooled states, including both positive and negative pressures, reveal (i) the existence of a non-monotonic temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low-temperature phase transition. The take-home message for the static aspects is that what seems to matter more than previously appreciated is local tetrahedral order, so that liquid water has features in common with SiO₂ and P, as well as perhaps Si and C. To better understand dynamic aspects of water, we focus on the role of the number of diffusive directions in the potential energy landscape. What seems to matter most is not values of thermodynamic parameters such as temperature T and pressure P, but only the value of a parameter characterizing the potential energy landscape—just as near a critical point what matters is not the values of T and P but rather the values of the correlation length.     

The role of the “Casimir force analogue” at the microscopic processes of crystallization and melting

Melting (crystallization), a phase transition from a crystalline solid to a liquid state, is a common phenomenon in nature. We suggest a new factor, “the Casimir force analogue”, to describe mechanisms of melting and crystallization. The Casimir force analogue is a force occurring between the surfaces of solid and liquid phases of metals caused by different energy density of phonons of these phases. It explains abrupt changes in geometry and thermodynamic parameters at a melting point. “The Casimir force analogue” helps to estimate latent melting heat and to gain an insight into a solid–liquid transition problem.     

A mathematical framework for critical transitions: Bifurcations, fast-slow systems and stochastic dynamics

Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms “critical transition” or “tipping point” have been used to describe this situation. Critical transitions have been observed in an astonishingly diverse set of applications from ecosystems and climate change to medicine and finance. The main goal of this paper is to give an overview which standard mathematical theories can be applied to critical transitions. We shall focus on early-warning signs that have been suggested to predict critical transitions and point out what mathematical theory can provide in this context. Starting from classical bifurcation theory and incorporating multiple time scale dynamics one can give a detailed analysis of local bifurcations that induce critical transitions. We suggest that the mathematical theory of fast-slow systems provides a natural definition of critical transitions. Since noise often plays a crucial role near critical transitions the next step is to consider stochastic fast-slow systems. The interplay between sample path techniques, partial differential equations and random dynamical systems is highlighted. Each viewpoint provides potential early-warning signs for critical transitions. Since increasing variance has been suggested as an early-warning sign we examine it in the context of normal forms analytically, numerically and geometrically; we also consider autocorrelation numerically. Hence we demonstrate the applicability of early-warning signs for generic models. We end with suggestions for future directions of the theory.     

Hydrodynamics and phases of flocks

We review the past decade’s theoretical and experimental studies of flocking: the collective, coherent motion of large numbers of self-propelled “particles” (usually, but not always, living organisms). Like equilibrium condensed matter systems, flocks exhibit distinct “phases” which can be classified by their symmetries. Indeed, the phases that have been theoretically studied to date each have exactly the same symmetry as some equilibrium phase (e.g., ferromagnets, liquid crystals). This analogy with equilibrium phases of matter continues in that all flocks in the same phase, regardless of their constituents, have the same “hydrodynamic”—that is, long-length scale and long-time behavior, just as, e.g., all equilibrium fluids are described by the Navier-Stokes equations. Flocks are nonetheless very different from equilibrium systems, due to the intrinsically nonequilibrium self-propulsion of the constituent “organisms.” This difference between flocks and equilibrium systems is most dramatically manifested in the ability of the simplest phase of a flock, in which all the organisms are, on average moving in the same direction (we call this a “ferromagnetic” flock; we also use the terms “vector-ordered” and “polar-ordered” for this situation) to exist even in two dimensions (i.e., creatures moving on a plane), in defiance of the well-known Mermin-Wagner theorem of equilibrium statistical mechanics, which states that a continuous symmetry (in this case, rotation invariance, or the ability of the flock to fly in any direction) can not be spontaneously broken in a two-dimensional system with only short-ranged interactions. The “nematic” phase of flocks, in which all the creatures move preferentially, or are simply oriented preferentially, along the same axis, but with equal probability of moving in either direction, also differs dramatically from its equilibrium counterpart (in this case, nematic liquid crystals). Specifically, it shows enormous number fluctuations, which actually grow with the number of organisms faster than the “law of large numbers” obeyed by virtually all other known systems. As for equilibrium systems, the hydrodynamic behavior of any phase of flocks is radically modified by additional conservation laws. One such law is conservation of momentum of the background fluid through which many flocks move, which gives rise to the “hydrodynamic backflow” induced by the motion of a large flock through a fluid. We review the theoretical work on the effect of such background hydrodynamics on three phases of flocks—the ferromagnetic and nematic phases described above, and the disordered phase in which there is no order in the motion of the organisms. The most surprising prediction in this case is that “ferromagnetic” motion is always unstable for low Reynolds-number suspensions. Experiments appear to have seen this instability, but a quantitative comparison is awaited. We conclude by suggesting further theoretical and experimental work to be done.     

醋酸N-正辛基吡啶离子液体在不同溶剂中的荧光光谱分析

离子液体具有熔点低、可忽略的蒸气压、电化学窗口宽、热稳定性高和良好的导电性等独特性能,引起了化学工业和相关领域的广泛关注。离子液体具有低蒸气压,不会造成空气污染,但这并不意味着它们对环境完全无害。大多数离子液体易溶于水,可能会因为意外泄漏或通过污水进入水生环境。常用离子液体[BMIM][PF₆]和[BMIM][BF₄]的水溶液中,很容易形成氢氟酸,磷酸,具有一定的腐蚀性。将离子液体列为绿色溶剂,也需要提供其关于代谢和降解的毒性、生态毒性研究数据,或者其对环境影响的数据,离子液体在不同溶剂中的检测方法是非常重要的。离子液体的光谱分析法用量较少、方法简单、结果准确。离子液体和许多有机溶剂互溶,可形成均一、稳定的溶液。荧光检测法具有灵敏度高,选择性好,线性范围宽和受外界干扰少等优点。本工作研究了醋酸N-正辛基吡啶（OP-OAc）离子液体在水、乙醇、乙腈、乙酸等4种溶剂中的荧光光谱。研究结果表明,OP-OAc离子液体在不同溶剂中的荧光强度：I_乙酸＞I_乙腈＞I_乙醇＞I_水;最大发射波长的大小顺序：λ_{em, 水}＞λ_{em, 乙醇}＞λ_{em, 乙腈}＞λ_{em, 乙酸};它们的最大发射波长相对于激发波长发生红移;水中OP-OAc的荧光强度与浓度存在较高的相关性;当加入的甲醇、乙醇、乙腈溶剂不断增加时,OP-OAc离子液体的荧光强度增加,溶剂与水的比例为8∶2时,OP-OAc离子液体的荧光强度最强,溶剂的比例超过80%时,荧光强度突然降低;水中OP-OAc离子液体在pH 10时,荧光强度最高,在pH 14时,荧光强度最低。     

Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem

Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.     

Correlated randomness and switching phenomena

One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. Further, many of these processes and structures have the remarkable feature of “switching” from one behavior to another as if by magic. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at some of the many spatial and temporal patterns in biology, medicine, and economics and even begin to characterize the switching phenomena that enables a system to pass from one state to another. Inspired by principles developed by A. Nihat Berker and scores of other statistical physicists in recent years, we discuss some applications of correlated randomness to understand switching phenomena in various fields. Specifically, we present evidence from experiments and from computer simulations supporting the hypothesis that water’s anomalies are related to a switching point (which is not unlike the “tipping point” immortalized by Malcolm Gladwell), and that the bubbles in economic phenomena that occur on all scales are not “outliers” (another Gladwell immortalization). Though more speculative, we support the idea of disease as arising from some kind of yet-to-be-understood complex switching phenomenon, by discussing data on selected examples, including heart disease and Alzheimer disease.     

液体-液体相变与反常特性

绝大多数物质的液态密度随温度降低而增大,即常见的热胀冷缩现象.但存在一类物质,如水及第四主族的硅、锗等,其液态密度在一定温度范围内随温度的升高而增大,即密度反常现象.此外,该类物质还存在动力学反常(密度越大粒子运动越快)、热力学反常(热力学量的涨落随温度降低而升高)等其他反常特性.这类材料的化学性质千差万别,但却具有相似的物理反常特性.进一步的理论研究发现部分材料具有两种液态,即高密度液态和低密度液态,两者之间存在一级相变.因此,反常特性与液体-液体相变是否有直接关联是一个值得深入研究的课题.本文主要介绍了具有液体-液体相变的一类材料及其反常特性,包括高温高压下氢的液体-液体相变及其超临界现象,镓的反常特性及其与液体-液体相变的关联等.     

Phantom Friedmann cosmologies and higher-order characteristics of expansion

We discuss a more general class of phantom (p < −?) cosmologies with various forms of both phantom (w < −1), and standard (w > −1) matter. We show that many types of evolution which include both Big-Bang and Big-Rip singularities are admitted and give explicit examples. Among some interesting models, there exist non-singular oscillating (or “bounce”) cosmologies, which appear due to a competition between positive and negative pressure of variety of matter content. From the point of view of the current observations the most interesting cosmologies are the ones which start with a Big-Bang and terminate at a Big-Rip. A related consequence of having a possibility of two types of singularities is that there exists an unstable static universe approached by the two asymptotic models—one of them reaches Big-Bang, and another reaches Big-Rip. We also give explicit relations between density parameters Ω and the dynamical characteristics for these generalized phantom models, including higher-order observational characteristics such as jerk and “kerk.” Finally, we discuss the observational quantities such as luminosity distance, angular diameter, and source counts, both in series expansion and explicitly, for phantom models. Our series expansion formulas for the luminosity distance and the apparent magnitude go as far as to the fourth-order in redshift z term, which includes explicitly not only the jerk, but also the “kerk” (or “snap”) which may serve as an indicator of the curvature of the universe.     

Lorenzian analysis of infinite Poissonian populations and the phenomena of Paretian ubiquity

The Lorenz curve is a universally calibrated statistical tool measuring quantitatively the distribution of wealth within human populations. We consider infinite random populations modeled by inhomogeneous Poisson processes defined on the positive half-line—the randomly scattered process-points representing the wealth of the population-members (or any other positive-valued measure of interest such as size, mass, energy, etc.). For these populations the notion of “macroscopic Lorenz curve” is defined and analyzed, and the notion of “Lorenzian fractality” is defined and characterized. We show that the only non-degenerate macroscopically observable Lorenz curves are power-laws manifesting Paretian statistics—thus providing a universal “Lorenzian explanation” to the ubiquitous appearance of Paretian probability laws in nature.     

Measurement of the optical absorption coefficient for liquid based on optical microfiber

An inline measuring method of the optical absorption coefficient for liquid based on optical microfiber (OM) is studied. If an OM is immersed into absorptive liquid, the additional loss of the OM will increase. We have analyzed the relationship between the additional loss of the OMs and the absorption coefficients of the liquids, and found that the OM with determinate construction will be useful for measuring the absorption coefficients of the liquid whose refractive index is lower than that of the OM. Two OM samples are prepared to measure the absorption coefficient of pure water. A supercontinuum source is launched into the OM sample which is immersed into pure water, and absorption spectrum from 1400 to 1700 nm has been achieved by monitoring the additional loss. The trend of the absorption spectrum is similar with that of the reported result, showing that the inline measurement of the optical absorption coefficient is a feasible method for those lower refractive index liquids.     

Liquid polyamorphism: Possible relation to the anomalous behaviour of water

We present evidence from experiments and computer simulations supporting the hypothesis that water displays polyamorphism, i.e., water separates into two distinct liquid phases. This concept of a new liquid-liquid phase transition is finding application to other liquids as well as water, such as silicon and silica. Specifically, we investigate, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point in (i) Two models of water, TIP5P and ST2, which display a first order liquid-liquid phase transition at low temperatures; (ii) the Jagla model, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions; and (iii) A Hamiltonian model of water where the idea of two length/energy scales is built in. This model also displays a first order liquid-liquid phase transition at low temperatures besides the first order liquid-gas phase transition at high temperatures. We find a correlation between the dynamic fragility crossover and the locus of specific heat maxima C_P^max (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesised liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between C_P^max and the dynamic crossover is not limited to the case of water, a hydrogen bonded network liquid, but is a more general feature of crossing the Widom line, an extension of the first-order coexistence line in the supercritical region. Dedicated to Armin Bunde on the occasion of his 60th birthday.     

Rotational spectra, conformational structures and dipole moments of 2-(ethylthio)ethanol by jet-cooled FTMW and ab initio calculations

The rotational spectra of three low-energy conformers of 2-(ethylthio)ethanol also known as ethyl 2-hydroxyethylsulfide or hydroxyethyl ethyl sulfide (HOEES), together with the monosubstituted ¹³C and ³⁴S isotopic forms of the two lowest energy conformers, have been measured in a molecular beam using a pulsed-nozzle Fourier-transform microwave spectrometer. To search for the likely conformational structures, ab initio calculations were performed at the MP2/6-31G* level for reduced dimensionality potential energy mapping and at the MP2=FULL/6-311G** and B3LYP=FULL/6-311G** levels for full structural optimization and electronic energy calculations of possible lower energy conformers. In all, five low-energy conformers, each of C₁ point group symmetry, were located in the ab initio search with complete information obtained on rotational constants, dipole moments, and structures. Rotational constants for three of the conformers agree well with the experimental observations, leaving the other two with no experimental partners. The three having experimental matches display relatively open “chain-like” structures corresponding to TG-, and GG-like forms, while the two with no experimental matches display relatively closed or “folded” structures with significantly different rotational constants. Although results using different ab initio level theories with and without zero point energy corrections alter the conformer energy ordering slightly, the no-match conformers always stay in the lower energy group, leaving an unsolved question as to why these lower energy conformers with “folded-like” structures were not observed in the jet-cooled FTMW spectra.     

Wavepacket dynamics, quantum reversibility, and random matrix theory

We introduce and analyze the physics of “driving reversal” experiments. These are prototype wavepacket dynamics scenarios probing quantum irreversibility. Unlike the mostly hypothetical “time reversal” concept, a “driving reversal” scenario can be realized in a laboratory experiment, and is relevant to the theory of quantum dissipation. We study both the energy spreading and the survival probability in such experiments. We also introduce and study the “compensation time” (time of maximum return) in such a scenario. Extensive effort is devoted to figuring out the capability of either linear response theory or random matrix theory (RMT) to describe specific features of the time evolution. We explain that RMT modeling leads to a strong non-perturbative response effect that differs from the semiclassical behavior.     

Heterophase dislocations — An approach towards interpreting high temperature grain boundary behavior

When the conditions of full thermodynamic equilibrium are added to the conventional linear elastic theory of dislocations a hybrid concept of “heterophase” dislocations arises. As developed here, heterophase dislocation theory provides a self-consistent method for calculating the core configuration, energy, and stress-strain field which minimize the thermodynamic potential of a dislocated crystal. Simple grain boundaries in crystals near the melting point are treated as constrained arrays of heterophase misfit dislocations with a liquid-like core phase similar to, but not identical with the properties of ordinary liquid phase. Measurements of the properties and behavior of {011&#x0304;} tilt boundaries in bismuth crystals near the melting point show that the new theory accounts accurately for the energetic dependence on tilt misorientation in the range 0° to 6°, and then deviates from the observed dependence. The new theory also permits prediction of a structural transition in grain boundaries which is extremely sensitive to the density of misfit dislocations. This transition, predicted to occur in bismuth at a tilt misorientation of 15° was also confirmed by hot-stage electron microscopy.     

Statistical dynamics of religion evolutions

A religion affiliation can be considered as a “degree of freedom” of an agent on the human genre network. A brief review is given on the state of the art in data analysis and modelization of religious “questions” in order to suggest and if possible initiate further research, after using a “statistical physics filter”. We present a discussion of the evolution of 18 so-called religions, as measured through their number of adherents between 1900 and 2000. Some emphasis is made on a few cases presenting a minimum or a maximum in the investigated time range—thereby suggesting a competitive ingredient to be considered, besides the well accepted “at birth” attachment effect. The importance of the “external field” is still stressed through an Avrami late stage crystal growth-like parameter. The observed features and some intuitive interpretations point to opinion based models with vector, rather than scalar, like agents.     

Physics of strongly coupled quark-gluon plasma

This review covers our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in: (i) explaining the RHIC data by hydrodynamics; (ii) describing lattice data using electric-magnetic duality; (iii) understanding of gauge-string duality known as AdS/CFT and its application for “conformal” plasma. In view of the interdisciplinary nature of the subject, we include a brief introduction into several topics “for pedestrians”. Some fundamental questions addressed are: Why is sQGP such a good liquid? What is the nature of (de)confinement and what do we know about “magnetic” objects creating it? Do they play any important role in sQGP physics? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical “gravity dual” to heavy ion collisions?     

Piezonuclear reactions - do they really exist?

In a number of recent articles in this journal F. Cardone and collaborators have claimed the observation of several striking nuclear phenomena which they attribute to “piezonuclear reactions”. One such claim [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 1956] is that subjecting a solution of ²²⁸Th to cavitation leads to a “transformation” of thorium nuclei that is 10⁴ times faster than the normal nuclear decay for this isotope. In a “Comment” [G. Ericsson, S. Pomp, H. Sjöstrand, E. Traneus, Phys. Lett. A 373 (2009) 3795] to the thorium work, we have criticized the evidence provided for this claim. In a “Reply” [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 3797] Cardone et al. answer only some minor points but avoid addressing the real issue. The information provided in their Reply displays a worrying lack of control of their experimental situation and the data they put forward as evidence for their claims. We point out several shortcomings and errors in the described experimental preparations, set-up and reporting, as well as in the data analysis. We conclude that the evidence presented by Cardone et al. is insufficient to justify their claims of accelerated thorium decay (by “piezonuclear reactions” or otherwise).     

Acoustic emission spectra and sonochemical activity in a 36 kHz sonoreactor

During ultrasound-induced cavitation in liquids, acoustic emissions at fundamental and harmonic frequencies can be detected. The effect of acoustic emissions at harmonic frequencies on the sonochemical and sonophysical activities has not been explored, especially in large-scale sonoreactors. In this study, the acoustic emissions in the range, 0-250 kHz in a 36 kHz sonoreactor with varying liquid heights were studied and compared with the sonochemical activities. The acoustic pressures at both fundamental and harmonics decreased drastically as the liquid height was increased due to the attenuation of sound energy. It was observed that the increase in input power resulted in only an increase in the acoustic emissions at derivative frequencies such as, harmonics and subharmonics. The sonochemical activity, evaluated in terms of sonochemiluminescence and H₂O₂ yield, was not significantly enhanced at higher input power levels. This suggests that at higher power levels, the “extra” acoustic energy is not effectively used to generate primary cavitation activity; rather it is converted to generate acoustic emissions at harmonic and subharmonic frequencies. This is an important observation for the design of energy efficiency large-scale sonochemical reactors.     

Time evolution of diffusion fringes in the Christiansen effect

When laser radiation is allowed to fall at the diffusion region separating two liquids in a Christiansen filter, a new fringe pattern appears. We termed it as “diffusion fringes”. In the present work, we have studied this interference fringe pattern and its time evolution. It has been observed that there is a definite co-relation between the shape of the fringe pattern and the width of the diffusion region. The time evolution of this fringe patterns indicates that as diffusion region increases the circular fringe becomes elliptical and finally straight. It is believed that a detailed investigation of these diffusion fringes will throw much needed light not only on the theory of the Christiansen effect but also on the rate of diffusion between two molecules.