Comparative molecular dynamics and Monte Carlo study of statistical properties for coarse-grained heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.     

Thermodynamics and kinetics of a Gō proteinlike heteropolymer model with two-state folding characteristics

We present results of Monte Carlo computer simulations of a coarse-grained hydrophobic-polar Gō-like heteropolymer model and discuss thermodynamic properties and kinetics of an exemplified heteropolymer, exhibiting two-state folding behavior. It turns out that general, characteristic folding features of realistic proteins with a single free-energy barrier can also be observed in this simplified model, where the folding transition is primarily driven by the hydrophobic force.     

Nonradial large solutions of sublinear elliptic problems

Let p be a nonnegative locally bounded function on , N3, and 0<γ<1. Assuming that the oscillation sup_|x|=rp(x)−inf_|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)u^γ admits a positive solution in satisfying lim_|x|→∞u(x)=∞ if and only if

     

3G-inequality for planar domains

The 3G-inequality for Green functions g _D on arbitrary bounded domains in ${{\mathbb{R}}^2}$ , which Bass and Burdzy (Probab Theory Relat Fields 101(4):479–493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin-off is an upper estimate of g _D on subdisks B′ of an open disk B in terms of g _B divided by the capacity of ${B'\setminus D}$ with respect to B.     

Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model

The tricritical behavior of the two-dimensional q-state Potts model with vacancies for 0q4 is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The known close connection between the critical properties of the pure model and the tricritical properties of the diluted model is shown to be reflected in an intimate relation between Fortuin–Kasteleyn and geometrical clusters: the same transformation mapping the two critical regimes onto each other also maps the two cluster types onto each other. The map conserves the central charge, so that both cluster types are in the same universality class. The geometrical picture is supported by a Monte Carlo simulation of the high-temperature representation of the Ising model (q=2) in which closed graph configurations are generated by means of a Metropolis update algorithm involving single plaquettes.     

Application of the multicanonical multigrid Monte Carlo method to the two-dimensional φ4: Autocorrelations and interface tension: Autocorrelations and interface tension

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar ⁴ on a square lattice. To investigate the peformance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard mlticanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from highstatistics histograms of the magnetization applying histogram reweighting techniques.     

Traceable property values of in-house reference materials

The traceability of in-house reference materials (IHRM) is discussed. It is shown that a systematic error in results of a measured value, specific to a measurement method or to a laboratory developing an IHRM, can be overcome if a comparative approach to IHRM characterization is used. A traceability chain of the value carried by the IHRM to the value carried by the reference material with higher metrological status and sufficiently similar matrix (for example, a certified reference material – CRM according to ISO Guide 30) is helpful in such a case. The chain is realized when the IHRM samples are analysed simultaneously with the CRM samples under the same conditions. This and other traceability chains necessary for the IHRM development are examined as the measurement information sources.