Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations and integral equations (Rogers-Young, Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, $D$, has a maximum at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. In the pressure-temperature phase-diagram the line of extrema in diffusivity is outside of TMD line. Although in this interparticle potential lacks directionality, this is the same behavior observed in SPC/E water.Comment: 16 page

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Enhanced bioremediation of subsurface contamination: Enzyme recruitment and redesign

Subsurface systems containing radionuclide, heavy metal, and organic wastes must be carefully attended to avoid further impacts to the environment or exposures to human populations. It is appropriate, therefore, to invest in basic research to develop the requisite tools and methods for addressing complex cleanup problems. The rational modification of subsurface microoganisms by enzyme recruitment and enzyme design, in concert with engineered systems for delivery of microorganisms and nutrients to the contaminated zone, are potentially useful tools in the spectrum of approaches that will be required for successful remediation of deep subsurface contamination

Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

Implementation of the Hierarchical Reference Theory for simple one-component fluids

Combining renormalization group theoretical ideas with the integral equation approach to fluid structure and thermodynamics, the Hierarchical Reference Theory is known to be successful even in the vicinity of the critical point and for sub-critical temperatures. We here present a software package independent of earlier programs for the application of this theory to simple fluids composed of particles interacting via spherically symmetrical pair potentials, restricting ourselves to hard sphere reference systems. Using the hard-core Yukawa potential with z=1.8/sigma for illustration, we discuss our implementation and the results it yields, paying special attention to the core condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio

Supporting parent-child conversations in a history museum

BACKGROUND: Museums can serve as rich resources for families to learn about the social world through engagement with exhibits and parent-child conversation about exhibits. AIMS: This study examined ways of engaging parents and child about two related exhibits at a cultural and history museum. Sample participants consisted of families visiting the Animal Antics and the Gone Potty exhibits at the British Museum. METHODS: Whilst visiting two exhibits at the British Museum, 30 families were assigned to use a backpack of activities, 13 were assigned to a booklet of activities, and 15 were assigned to visit the exhibits without props (control condition). RESULTS: Compared to the families in the control condition, the interventions increased the amount of time parents and children engaged together with the exhibit. Additionally, recordings of the conversations revealed that adults asked more questions related to the exhibits when assigned to the two intervention conditions compared to the control group. Children engaged in more historical talk when using the booklets than in the other two conditions. CONCLUSIONS: The findings suggest that providing support with either booklets or activities for children at exhibits may prove beneficial to parent-child conversations and engagement with museum exhibits

More is the Same; Phase Transitions and Mean Field Theories

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.Comment: 25 pages, 6 figure

Multifractal properties of return time statistics

Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets of dimensions is established. Theoretical analysis and numerical examples of dynamical systems in the class of Iterated Functions are presented.Comment: 4 pages, 3 figure

Weak point disorder in strongly fluctuating flux-line liquids

We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid of relativistic charged bosons in 2+1 dimensions [P. Benetatos and M. C. Marchetti, Phys. Rev. B 64, 054518, (2001)]. In this model, flux lines are allowed to be arbitrarily curved and can even form closed loops. Point defects can be scalar or polar. In the latter case, the direction of their dipole moments can be random or correlated. Within the Gaussian approximation of our hydrodynamic model, we calculate disorder-induced corrections to the correlation functions of the flux-line fields and the elastic moduli of the flux-line liquid. We find that scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease the tilt modulus.Comment: 15 pages, submitted to Pramana-Journal of Physics for the special volume on Vortex State Studie

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page