Conformal Invariance and Conserved Quantity for?the?Nonholonomic System of Chetaev’s Type

In this paper the definition of conformal invariance and determining equation for the holonomic system which correspond to a nonholonomic system of Chetaev’s type are provided. Conformal factor expression is deduced through relationship between a system’s conformal invariance and Lie symmetry. The necessary and sufficient condition that the system’s conformal invariance would be Lie symmetry under transformations by the infinitesimal one-parameter transformation group is obtained. The conformal invariance of weak and strong Lie symmetry for the nonholonomic system of Chetaev’s type is given using restriction equations and additional restriction equations. And the system’s corresponding conserved quantity is derived with the aid of a structure equation that gauge function satisfied. Lastly, an example is taken to illustrate the application of the result.     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

Preliminary Monte Carlo Results for the Three-Dimensional Holstein Model

Monte Carlo simulations are used to study the three-dimensional Holstein model. The relationship between the band filling and the chemical potential is obtained for various phonon frequencies and temperatures. The energy of a single electron or a hole is also calculated as a function of the lattice momenta.     

Fast Monte Carlo inversion for extracting the optical properties of tubular tissues

Reconstruction of absorption coefficientμ_a and scattering coefficientμ_a is very important for applications of diffuse optical tomography and near infrared spectroscopy.Aiming at the early cancer detection of cervix and stomach,we present a fast inverse Monte-Carlo scheme for extractingμ_a andμ_s of a tubular tissue from the measurement on frequency domain.Results show that the computation time for reconstructing one set ofμ_a andμ_s is less than 1 min and the relative errors in reconstruction are less than±10% for the optical properties of normal cervical tissue and precancerous lesions.     

A Monte Carlo study for the shielding of γ backgrounds induced by radionuclides for CDEX

The CDEX (China Dark matter EXperiment) Collaboration will carry out a direct search for WIMPs (Weakly Interacting Massive Particles) using an Ultra-Low Energy Threshold High Purity Germanium (ULE-HPGe) detector at the CJPL (China JinPing deep underground Laboratory). A complex shielding system was designed to reduce backgrounds and a detailed GEANT4 Monte Carlo simulation was performed to study the achievable reduction of γ rays induced by radionuclides and neutron backgrounds by D(γ,n)p reaction. Furthermore, the upper level of allowed radiopurity of shielding materials was estimated under the constraint of the expected goal. Compared with the radiopurity reported by other low-background rare-event experiments, it indicates that the shielding used in the CDEX can be made out of materials with obtainable radiopurity.     

Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.     

A WENO-solver for the transients of Boltzmann–Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods

In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann–Poisson system for semiconductor devices. We follow the work in Fatemi and Odeh [9] and in Majorana and Pidatella [16] to formulate the Boltzmann–Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today’s computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper.     

Integrable and Conformal Boundary Conditions for \widehat{s\ell}(2) A–D–E Lattice Models and Unitary Minimal Conformal Field Theories

Integrable boundary conditions are studied for critical A–D–E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley–Lieb algebra and fusion, a set of boundary Boltzmann weights which satisfies the boundary Yang–Baxter equation is obtained for each boundary condition. When appropriately specialized, these boundary weights, each of which depends on three spins, decompose into more natural two-spin edge weights. The specialized boundary conditions for the A–D–E cases are naturally in one-to-one correspondence with the conformal boundary conditions of $\widehat{s\ell }$ (2) unitary minimal conformal field theories. Supported by this and further evidence, we conclude that, in the continuum scaling limit, the integrable boundary conditions provide realizations of the complete set of conformal boundary conditions in the corresponding field theories.     

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.     

Monte Carlo Simulation of the BEPCⅡ/BESⅢ Backgrounds—Beam-Gas Interactions

The beam-gas backgrounds simulation of the BESⅢ, including the theory and the results is introduced. The results show that, after masking on the storage ring, the detector backgrounds are in safe level. The results can guide the design and construction of the BEPCⅡ-BESⅢ.     

Effective Dynamics for a Kinetic Monte–Carlo Model with Slow and Fast Time Scales

We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a one-dimensional potential energy landscape which has some small and some large barriers, the latter dividing the state space into metastable regions. In the limit of infinitely large barriers, we identify the effective dynamics between these macro-states, and prove the convergence of the process towards a kinetic Monte Carlo model. We next consider a third model, which consists of a system of two particles. The state of each particle evolves on a fast time-scale while conserving their respective energy. In addition, the particles can exchange energy on a slow time scale. Considering the energy of the first particle, we identify its effective dynamics in the limit of asymptotically small ratio between the characteristic times of the fast and the slow dynamics. For all models, our results are illustrated by representative numerical simulations.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

OPTIS—An Einstein Mission for Improved Tests of Special and General Relativity

The mission OPTIS aims at improving tests of the foundations of Special and General Relativity by up to three orders of magnitude. The individual tests concern the isotropy and constancy of the speed of light, the time dilation (or Doppler effect), the universality of the gravitational redshift with various combinations of high precision clocks. Furthermore, laser tracking and a laser link allows a strongly improved measurement of the gravitomagnetic Lense–Thirring effect, of the gravitoelectric Einstein perigee advance, of the gravitational redshift, and a search for deviations from Newtonian gravity.For this mission, technologies are required which have been used recently to carry through the most precise tests of Special Relativity. The precision of these tests can be further increased under space conditions thanks to longer integration times, larger changes in the orbital velocity, and larger differences of the gravitational potential. Furthermore, very precise laser tracking and linking of satellites is a well established technique and will provide, in combination with the active drag–free control system, very accurate orbit data. The core technologies for OPTIS are optical cavities, highly stabilized lasers, capacitive gravitational reference sensors, drag–free control, ion clocks, frequency combs, and laser tracking systems. These technologies are also key technologies for other future missions.     

Development and Application of Fast Monte Carlo Simulation Method for Beijing τ-Charm Factory (BTCF)

Based on the existing concept design and the expected performance of the detector at the future τ-charm factory,a fast Monte Carlo simulation program package using the BES software frame and data structure has been devcloped.Vadous important and/or interesting physics issues have been simulated by using this method,and a series of important physics results have been got.The design idea,the program frame,and the advantages of this method have been described.One can conclude that this Monte Carlo simulation method can greatly save CPU and disk space,and is specially suitable for BES users.The physics results obtained from the simulation demonstrate that it is essential to build the BTCF.     

On Convergence to SLE<Subscript>6</Subscript> I: Conformal Invariance for Certain Models of the Bond-Triangular Type

We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511–565, 2007).