Search results for " Statistical Mechanics"
showing 10 items of 557 documents
Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?
2018
Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle $(\Theta)$ on the droplet radius $(R)$ of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on "thermodynamic" observables, e.g., chemical potential, excess density due to the droplet, etc., is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation $[\Th…
Effect of mixing and spatial dimension on the glass transition
2009
We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparitie…
Fractional Laplacians and Levy flights in bounded domains
2018
We address L\'{e}vy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Laplacian (and thence the induced random process) should actually be. Versions considered are: restricted Dirichlet, spectral Dirichlet and regional (censored) fractional Laplacians. The affiliated random processes comprise: killed, reflected and conditioned L\'{e}vy flights, in particular those with an infinite life-time. The related concept of quasi-stationary distributions is briefly mentioned.
Monte Carlo Tests of Nucleation Concepts in the Lattice Gas Model
2013
The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasi-static) cluster (droplet) growth over a free energy barrier $\Delta F^*$, constructed in terms of a balance of surface and bulk term of a "critical droplet" of radius $R^*$, implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius $R=R^*$. For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. U…
Statistics of reversible transitions in two-state trajectories in force-ramp spectroscopy
2014
A possible way to extract information about the reversible dissociation of a molecular adhesion bond from force fluctuations observed in force ramp experiments is discussed. For small loading rates the system undergoes a limited number of unbinding and rebinding transitions observable in the so-called force versus extension (FE) curves. The statistics of these transient fluctuations can be utilized to estimate the parameters for the rebinding rate. This is relevant in the experimentally important situation where the direct observation of the reversed FE-curves is hampered, e.g. due to the presence of soft linkers. I generalize the stochastic theory of the kinetics in two-state models to the…
Single-layer metal-on-metal islands driven by strong time-dependent forces
2012
Non-linear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semi-empirical lattice model and use master equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of int…
Liquid methane at extreme temperature and pressure: Implications for models of Uranus and Neptune
2012
We present large scale electronic structure based molecular dynamics simulations of liquid methane at planetary conditions. In particular, we address the controversy of whether or not the interior of Uranus and Neptune consists of diamond. In our simulations we find no evidence for the formation of diamond, but rather sp2-bonded polymeric carbon. Furthermore, we predict that at high tem- perature hydrogen may exist in its monoatomic and metallic state. The implications of our finding for the planetary models of Uranus and Neptune are in detail discussed.
Ion-ion correlation and charge reversal at titrating solid interfaces
2009
Confronting grand canonical titration Monte Carlo simulations (MC) with recently published titration and charge reversal (CR) experiments on silica surfaces by Dove et al. and van der Heyden it et al, we show that ion-ion correlations quantitatively explain why divalent counterions strongly promote surface charge which, in turn, eventually causes a charge reversal (CR). Titration and CR results from simulations and experiments are in excellent agreement without any fitting parameters. This is the first unambiguous evidence that ion-ion correlations are instrumental in the creation of highly charged surfaces and responsible for their CR. Finally, we show that charge correlations result in "a…
Role of noise in a market model with stochastic volatility
2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES ef…
Langevin Approach to Understand the Noise of Microwave Transistors
2004
A Langevin approach to understand the noise of microwave devices is presented. The device is represented by its equivalent circuit with the internal noise sources included as stochastic processes. From the circuit network analysis, a stochastic integral equation for the output voltage is derived and from its power spectrum the noise figure as a function of the operating frequency is obtained. The theoretical results have been compared with experimental data obtained by the characterization of an HEMT transistor series (NE20283A, by NEC) from 6 to 18 GHz at a low noise bias point. The reported procedure exhibits good accuracy, within the typical uncertainty range of any experimental determin…