Nonequilibrium statistical mechanics model showing self-sustained oscillations.

Historically, the development of equations of state for fluids has almost invariably followed the lead of the van der Waals (vdW) equation which includes an attraction term and a repulsion term. In this paper, using a simple statistical mechanics model, we introduce a parameter σ as both the power and a coefficient of the packing fraction y which locates at the numerator of the vdW attraction term. Then nine equations of state are constructed to solve the critical conditions and the main thermodynamic properties of pure substances at liquid-vapor equilibrium. As a result, the correct critical compressibility factors of Nitrogen, Argon, Carbon dioxide, Ethene, Methane, Oxygen, Propene, Water and Hydrogen, are obtained with an optimal choice of parameter σ. Good predictions of these equations to the liquid-vapor equilibrium properties below critical temperature are reported and compared with experimental data.

Several key problems previously analyzed by simulated annealing are well described by a simple two-state statistical mechanical model, equivalent to the one-dimensional Ising model, in conjunction with an Arrhenius type rate equation. With this model we develop an analytic solution for the optimal cooling strategy which computationally is much faster than the previously developed adaptive algorithm. In the long time limit the analytic solution reduces to the one cooling schedule which is sure to reach the ground state. Our model predictions are in good agreement with earlier numerical simulation results for optimal cooling schedules as well as for stationary and dynamic properties of system energy, heat capacity, and relaxation time.

Local signals in the energy landscape of collapsed helical proteins

The behavior of the inter-ionic potential of condensed liquid cesium in a wide temperature range

Following a review of the problem of stilbene isomerism an account is given of recent picosecond tinescale experiments on this system.Transient absorption methods are used to expose vibrational relaxation details for molecules in solution and streak camera measurements of fluorescence decay are presented to demonstrate the irreversibility of the Si (trans) decay.A simple statistical mechanical model is presented to describe the effect of viscosity on the twisting dynamics of trans-stilbene.A summary of recent experiments involving stilbene in the gas phase is presented.The isolated molecules twist very rapidly (15 ps at 265 nm excitation) and display characteristics typical of systems with a potential barrier.Finally the solution and gas phase processes are contrasted. INTRODUCTORY REVIEWIt is well known that substituted ethylenes can undergo cis-trans isomerism following optical excitation.A large literature already exists on this topic and the particular case of stilbenes (1,2-diphenylethylenes) was recently reviewed by Saltiel and coworkers (1).Phenyl substituted ethylenes received considerable attention from photochenists because their optical spectra are in the near ultraviolet, readily accessible to traditional light sources.The groundwork for understanding the photoisomerisn process in solutions was laid on the basis of conventional (pre-laser) experiments (1,2) but the intrinsic molecular steps involved are now known from vapor phase studies to be subnanosecond (3,4).The basic model for the isomerism is that a twisted, less conjugated form of tilbene is formed following optical excitation (5) .This twisted form may then undergo relaxation processes that result in both cis and trans structures (6).The solvent slows down the isomerization and at sufficiently low temperature or high viscosity the rate is found to be even slower than the natural radiative processes (7).The fluorescent properties of the system therefore can be used to monitor the isonerization.Saltiel and coworkers (8,9) have shown that the principal ultraviolet photochemistry of stilbeme arises from the singlet excited surface.The triplet state can be involved when sensitizers are present (9,10), and the ground state pathway requires moderately high temperatures (1,2).There is also evidence that isomerization is not the exclusive photoprocess since small yields of rearranged species have been reported (11).

The critical dynamics of charge-density waves (CDW's) just above the threshold for steady-state sliding motion are studied via a renormalization-group expansion in 4-\ensuremath{\epsilon} dimensions. This necessitates the simultaneous treatment of the long-wavelength low-frequency dynamics as well as the singular behavior associated with the jumps of local regions during which the local velocities become large. Scaling forms are obtained for response and correlation functions in the critical region, and exponent identities are derived. To leading order in \ensuremath{\epsilon}, the exponent \ensuremath{\zeta} of the CDW current ${\mathit{I}}_{\mathrm{CDW}}$\ensuremath{\sim}(V-${\mathit{V}}_{\mathit{T}}$${)}^{\mathrm{\ensuremath{\zeta}}}$ just above the threshold voltage ${\mathit{V}}_{\mathit{T}}$ is found to be \ensuremath{\zeta}=1-\ensuremath{\epsilon}/6+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), in reasonable agreement with recent numerical simulations in two and three dimensions. The spatial correlations in the local velocities of the CDW decay exponentially with a correlation length, which diverges with an exponent \ensuremath{\nu} exactly equal to 1/2. Nevertheless, finite-size scaling of many quantities will be determined by a different exponent ${\ensuremath{\nu}}_{\mathrm{FS}}$=1/2+\ensuremath{\epsilon}/8+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$)=2/d+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). The other exponents are related to \ensuremath{\zeta}, \ensuremath{\nu}, and ${\ensuremath{\nu}}_{\mathrm{FS}}$. Simple forms of long-wavelength low-frequency correlation and response functions in the moving phase are obtained to all orders in perturbation theory.

Simple statistical mechanical models are applied to calculate thermodynamic properties of liquid silicate- mixtures. From these models relative activities for binary silicate- mixtures have been derived both for structural units of equal size and for structural units of unequal size. Theoretical relative activities have been tested by using the limited experimental data on binary, or approximately binary, portions of the system with formulas for freezing-point depression and isothermal solubility for the condition . The experimental data for all systems except can be approximated by a simple regular solution theory with a negative heat of mixing. The existing data for require a much more complex solution theory. The qualitative agreement of theory with experiment is good but the quantitative agreement is only fair. It is impossible, however, to determine unequivocally the physical significance of the quantitative agreement on the basis of isothermal solubility and freezing-point depression without refinement of experimental data and heats of fusion for the silicates.

Consider two interacting sub-systems with nonoverlapping charge distributions. How can the properties of the combined system be expressed in terms of properties of the individual sub-systems alone? This general problem appears in a wide variety of physical, chemical, and biological systems [Joester 2003, Stone 1996, Moore 2001]. In this chapter we provide a prescription for addressing this issue by the computation of (i) response functions and (ii) correlation functions of spontaneous fluctuations of relevant degrees of freedom in the individual sub-systems. The computation of response and correlation functions is greatly simplified by using the density matrix in Liouville space [Mukamel 1995]. Hilbert and Liouville spaces offer very different languages for the description of nonlinear response. Computing dynamical observables in terms of the wavefunction in Hilbert space requires both forward and backward propagations in time. In contrast, the density matrix calculated in Liouville space should only be propagated forward. The choice is between following only the ket, moving it both forward and backward, or following the joint forward dynamics of the ket and the bra. Artificial time variables (Keldysh loops) commonly used in many-body theory [Haug 1996] are connected with the wavefunction. The density matrix which uses the real laboratory time throughout the calculation offers a more intuitive picture. Wavefunction-based theories calculate transition amplitudes, which by themselves are not observable. The density matrix, on the other hand directly calculates physical observables. Moreover, dephasing processes (damping of off-diagonal elements of the density matrix caused by phase fluctuations) which are naturally included into the Liouville space formulation may not be described in terms of the wavefunction. The “causality paradox” of TDDFT [Gross 1996] can be clearly resolved in Liouville space [Mukamel 2005]. In this chapter we present a method for expressing the joint response of two interacting sub-systems in terms of their correlation and response functions. This factorization appears quite naturally in Liouville space. The p order response of the individual systems is a linear combination of 2 distinct (p + 1)-point correlation functions known as Liouville space pathways [Mukamel 1995], which differ by whether the interaction at each time

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a beta-hairpin, the minimal structural element of the antiparallel beta-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, beta-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 2(15) possible conformations and 15 x 2(15) possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the beta-hairpin peptide.

Protein chains coil into alpha-helices and beta-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold. For the past 40 years, alpha-helix formation has been extensively investigated in synthetic and natural peptides, including by nanosecond kinetic studies. In contrast, the mechanism of formation of beta structures has not been studied experimentally. The minimal beta-structure element is the beta-hairpin, which is also the basic component of antiparallel beta-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a beta-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 micros at room temperature, which is about 30 times slower than the rate of alpha-helix formation. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a beta-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

A purely static characterisation of “atomic” versus “ionized” states is given in terms of the spectral properties of the pair reduced density matrix. These spectral properties can be analyzed in a simple model (a “short range electron” with classical “hard core protons”). In the model the Mott effect occurs at high density as a consequence of the reduction of particle fluctuations.

We use a combination of variable-temperature high-resolution synchrotron X-ray powder diffraction measurements and Monte Carlo simulations to characterise the evolution of two different types of ferroic multipolar order in a series of cyano elpasolite molecular perovskites. We show that ferroquadrupolar order in [C3N2H5]2Rb[Co(CN)6] is a first-order process that is well described by a 4-state Potts model on the simple cubic lattice. Likewise, ferrooctupolar order in [NMe4]2B[Co(CN)6] (B = K, Rb, Cs) also emerges via a first-order transition that now corresponds to a 6-state Potts model. Hence, for these particular cases, the dominant symmetry breaking mechanisms are well understood in terms of simple statistical mechanical models. By varying composition, we find that the effective coupling between multipolar degrees of freedom—and hence the temperature at which ferromultipolar order emerges—can be tuned in a chemically sensible manner.

In the present study, we performed molecular dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation length ξ(4)(t), the intensity χ(4)(t), and the lifetime τ(hetero)(t). We quantified all three quantities by means of the correlation functions of the particle dynamics, i.e., the four-point correlation functions, which are extended to the sheared condition. Here, to define the local dynamics, we used two time intervals t = τ(α) and τ(ngp); τ(α) is the α-relaxation time, and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. We discovered that all three quantities (ξ(4)(t), χ(4)(t), and τ(hetero)(t)) decrease as the shear rate γ of the steady shear flow increases. For the time interval t = τ(α), the scalings ξ(4)(τ(α))~γ(-0.08), χ(4)(τ(α))~γ(-0.26), and τ(hetero)(τ(α))~γ(-0.88) were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, we demonstrated that all three quantities in the sheared non-equilibrium state can be mapped onto those in the equilibrium state through the α-relaxation time τ(α). This finding means that the same relation between τ(α) and three quantities holds in both the equilibrium state and the sheared non-equilibrium state and therefore proposes that the dynamical heterogeneity can play a similar role in the drastic change of τ(α) due to not only the temperature but also the shear rate.

THERMINATOR: THERMal heavy-IoN generATOR