The main part of the global illumination problem of computer graphics is given by a Fredholm integral equation of the second kind, describing the light distribution in a closed environment. Calculating photorealistic images from that equation requires its kernel to be very complex and discontinuous. Due to this complexity Monte Carlo methods are an interesting tool for estimating a solution. In...

A brief review of the semi-classical Monte Carlo method for semiconductor device simulation is given, covering the standard Monte Carlo algorithms, variance reduction techniques, the self-consistent solution, and the physical semiconductor model including band structure and scattering mechanisms. The link between physically-based Monte Carlo methods and the numerical method of Monte Carlo integ...

We consider the approximation of d-dimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where d is large. We show that the convergence rate of quasi-Monte Carlo for the approximation of these integrals is O( √ logn/n). Since this is a worst case result, compared to the expected convergence rate O(n−1/2) of Monte Carlo, it shows the superiority of quas...

Introduction: Development of higher energy modalities such as positron emission tomography/computed tomography (PET/CT), has led to more complex shielding problems. This is due to several factors, such as the radiopharmaceutical relatively high-administered activity, high patient throughput, and high energies of 511 kilo-electron volt (keV) positron annihilation photon...

The internal energy of high-density hydrogen plasmas in the temperature range T = 10, 000 . . . 50, 000K is calculated by two different analytical approximation schemes (method of effective ion-ion interaction potential EIIP and Padé approach within the chemical picture PACH) and compared with path integral Monte Carlo results. Reasonable agreement between the results obtained from the three in...

Atomically thin 4 He lms of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T=0.5 K, using path integral Monte Carlo. We compute the binding energy of 4 He to the H 2 substrate as a function of 4 He coverage and obtain evidence of the prewetting transition. Density pro les perpendicular to the 4 He-H 2 interface are obtained, as well as the zero point motion and e e...

so that the error in I goes down as 1/ √ M and is smaller if the variance σ 2 f of f is smaller. For a one dimensional integration the Monte Carlo method is not compelling. However consider a d dimensional integral evaluated withM points. For a uniform mesh each dimension of the integral getsM1/d points, so that the separation is h = M−1/d . The error in the integration over one h cube is of or...

Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix, represented in PIMC by open paths. It is demonstrated how the restricted path integral Monte Carlo methods can be extended in order to deal with open paths in fe...

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H eff ({S i }) derived from the coherent-state integral is highly singular: the quasiprobability density exp(−βH eff), a Wigner function, imposes quantisation through derivatives of delta f...

Monte Carlo methods are extensively used in Nuclear Medicine to tackle a variety of problems that are difficult to study by an experimental or analytical approach. A review of the most recent tools allowing application of Monte Carlo methods in single photon emission tomography (SPET) and positron emission tomography (PET) is presented. To help potential Monte Carlo users choose a code, we pres...