scholarly journals Magnetic Field Distribution and Signal Decay in Functional MRI in Very High Fields (up to 9.4 T) Using Monte Carlo Diffusion Modeling

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
Bernd Michael Mueller-Bierl ◽  
Kamil Uludag ◽  
Philippe L. Pereira ◽  
Fritz Schick
Keyword(s):  
Monte Carlo ◽  
Field Strength ◽  
Boundary Conditions ◽  
Field Distribution ◽  
Three Dimensional ◽  
Time Step ◽  
Signal Decay ◽  
Step Procedure ◽  
Wide Range ◽  
Field Strengths

Extravascular signal decay rate R2 or R2∗as a function of blood oxygenation, geometry, and field strength was calculated using a Monte Carlo (MC) algorithm for a wider parameter range than hitherto by others. The relaxation rates of gradient-recalled-echo (GRE) and Hahn-spin-echo (HSE) imaging in the presence of blood vessels (ranging from capillaries to veins) have been computed for a wide range of field strengths up to 9.4 T and 50% blood deoxygenation. The maximum HSE decay was found to be shifted to lower radii in higher compared to lower field strengths. For GRE, however, the relaxation rate was greatest for large vessels at any field strength. In addition, assessments of computational reliability have been carried out by investigating the influence of the time step, the Monte Carlo step procedure, boundary conditions, the number of angles between the vessel and the exterior fieldB0, the influence of neighboring vessels having the same orientation as the central vessel, and the number of proton spins. The results were compared with those obtained from a field distribution of the vessel computed by an analytic formula describing the field distribution of an ideal object (an infinitely long cylinder). It was found that the time step is not critical for values equal to or lower than 200 microseconds. The choice of the MC step procedure (three-dimensional Gaussian diffusion, constant one- or three-dimensional diffusion step) also failed to influence the results significantly; in contrast, the free boundary conditions, as well as taking too few angles into account, did introduce errors. Next neighbor vessels with the same orientation as the main vessel did not contribute significantly to signal decay. The total number of particles simulated was also found to play a minor role in computing R2/ R2∗.

Monte Carlo Simulation of Precipitate Nucleation and Growth: Time Dependent Results

1988 ◽  
Vol 141 ◽  
Author(s):  
James P. Lavine ◽  
Gilbert A. Hawkins
Keyword(s):  
Monte Carlo ◽  
Crystalline Silicon ◽  
Three Dimensional ◽  
Nucleation Site ◽  
Nucleation And Growth ◽  
Lattice Points ◽  
Growth Time ◽  
Decay Kinetics ◽  
Time Step ◽  
Oxygen Atoms

AbstractA three-dimensional Monte Carlo computer program has been developed to study the heterogeneous nucleation and growth of oxide precipitates during the thermal treatment of crystalline silicon. In the simulations, oxygen atoms move on a lattice with randomly selected lattice points serving as nucleation sites. The change in free energy that the oxygen cluster would experience in gaining or losing one oxygen atom is used to govern growth or dissolution of the cluster. All the oxygen atoms undergo a jump or a growth decision during each time step of the anneal. The growth and decay kinetics of each nucleation site display interesting fluctuation phenomena. The time dependence of the cluster size generally differs from the expected 3/2 power law due to the fluctuations in oxygen arrival at and incorporation in a precipitate. Competition between growing sites and coarsening are observed.

scholarly journals A 3D particle Monte Carlo approach to studying nucleation

2017 ◽  
Author(s):  
Christoph Köhn ◽  
Martin Bødker Enghoff ◽  
Henrik Svensmark
Keyword(s):  
Monte Carlo ◽  
Sulphuric Acid ◽  
Nucleation Rate ◽  
Particle Density ◽  
Monte Carlo Model ◽  
Three Dimensional ◽  
Initial Particle ◽  
Time Step ◽  
Size Dependent ◽  
Discrete Nature

Abstract. The nucleation of sulphuric acid molecules plays a key role in the formation of aerosols. We here present a three dimensional particle Monte Carlo model to study the growth of sulphuric acid clusters as well as its dependence on the ambient temperature and the initial particle density.We initiate a swarm of sulphuric acid molecules with a size of 0.15 nm with densities between 107 and 108 cm−3 at temperatures of 200 and 300 K. After every time step, we update the position and velocity of particles as a function of size-dependent diffusion coefficients. If two particles encounter, we merge them and add their volumes and masses. Inversely, we check after every time step whether a polymer evaporates liberating a molecule.We present the spatial distribution as well as the size distribution calculated from individual clusters. We also calculate the nucleation rate of clusters with a radius of 0.85 nm as a function of time, initial particle density and temperature. For 200 K, the nucleation rate increases as a function of time; for 300 K we observe an interplay between clustering and evaporation and thus the oscillation of the nucleation rate around the mean nucleation rate. The nucleation rates obtained from the presented model agree well with experimentally obtained values which serves as a benchmark of our code. In contrast to previous nucleation models, we here present for the first time a code capable of tracing individual particles and thus of capturing the physics related to the discrete nature of particles.

Study on Grain Topology with Potts Model Monte Carlo Simulation

2014 ◽  
Vol 926-930 ◽  
pp. 1538-1541
Author(s):  
Hao Wang ◽  
Guo Quan Liu
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Potts Model ◽  
Three Dimensional ◽  
Wide Range ◽  
The Mean ◽  
Simulation Results ◽  
Number Of Faces ◽  
Grain Topology ◽  
Range Of Values

Three-dimensional normal grain growth has been simulated in scale 300×300×300 using the generally accepted Potts model Monte Carlo method. The studies of the topology of grains indicate that the mean number of faces in the grain network <f>=13.91 is similar to other simulation results, but higher than most of the experimental data which containing a wide range of values, i.e., <f>=11.16~13.93. The three-dimensional AboavWeaire law and Liu-Yu law are observed to hold, but the fit coefficient is different from the theory models.

Direct Simulation Monte Carlo Calculations of Three Dimensional Non-Continuum Gas Flows

2002 ◽  
Author(s):  
Fang Yan ◽  
Bakhtier Farouk ◽  
Jeremy Johnson
Keyword(s):  
Monte Carlo ◽  
Couette Flow ◽  
Three Dimensional ◽  
Direct Simulation Monte Carlo ◽  
Particle Removal ◽  
Direct Simulation ◽  
Transition Flow ◽  
Multiprocessor Computer ◽  
Wide Range ◽  
Simulation Monte Carlo

This paper describes the parallel implementation of a three-dimensional direct simulation Monte Carlo (DSMC) code using the OpenMP procedure on a shared memory multiprocessor computer. A dynamic domain decomposition is performed to maintain load balance among the threads. Performance tests are conducted to evaluate the effect of granularity on efficiency. It is shown that the parallel performance is dependent on the problem size. For larger-scale problems, better efficiency can be expected. Synchronization overhead due to data contention is reduced by re-arranging particle removal procedure. The parallel code is used to simulate flow through a rectangular channel with a high-speed moving wall (Couette flow). For high Knudsen (Kn) numbers, the Couette flow characteristics are found to be very different from their continuum counterparts. ‘Ultimate pressures’ are calculated for a wide range of Kn number flows. The variation of the ultimate pressure with Kn number is computed for given wall speed. Maximum compression ratio is obtained in the transition flow region.

Three‐dimensional elastic modeling by the Fourier method

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1184-1193 ◽  
Author(s):  
Moshe Reshef ◽  
Dan Kosloff ◽  
Mickey Edwards ◽  
Chris Hsiung
Keyword(s):  
Wave Velocity ◽  
Three Dimensional ◽  
P Wave ◽  
Velocity Variation ◽  
Difference Operators ◽  
Time Step ◽  
Current Time ◽  
Partial Differentiation ◽  
Wide Range ◽  
Spatial Grid

Earlier work on three‐dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress‐strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P‐wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S‐wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Computation of each time step begins by computing six strain components by performing nine spatial partial differentiation operations on the three displacement components from the previous time step. The six strains and two Lamé constants are linearly combined to yield six stress components. Nine spatial partial differentiation operations on the six stresses, three body forces, and density are used to compute second partial time derivatives of the three displacement components. Time stepping to obtain the three displacement components for the current time step is performed with second‐order difference operators. The modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. This modeling scheme is implemented on a four‐processor CRAY X‐MP computer system using the solid‐state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays. These features enable the modeling of a wide range of seismic surveys. Numerical and analytic results are presented.

LATTICE SPIN SIMULATIONS OF TOPOLOGICAL DEFECTS IN BIAXIAL NEMATIC FILMS WITH HOMEOTROPIC SURFACE ALIGNMENT

2013 ◽  
Vol 24 (05) ◽  
pp. 1350026 ◽  
Author(s):  
GOURIPEDDI SAI PREETI ◽  
CLAUDIO ZANNONI ◽  
CESARE CHICCOLI ◽  
PAOLO PASINI ◽  
VANKA S. S. SASTRY
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Topological Defects ◽  
Monte Carlo Study ◽  
Surface Alignment ◽  
Lattice Spin ◽  
Polarized Microscopy ◽  
Wide Range ◽  
Microscopy Images ◽  
Biaxial Nematic

We present a detailed Monte Carlo study of the effects of biaxiality on the textures of nematic films with specific homeotropic boundary conditions. We have used the Straley generalized Hamiltonian for a wide range of biaxial parameters and the differences obtained in the polarized microscopy images are analyzed for the various cases.

Monte Carlo calculation of the energy parameters and spatial distribution of the cathodic arc ions while passing through the macro-particles filters

2018 ◽  
Vol 1 (1) ◽  
pp. 30-34 ◽  
Author(s):  
Alexey Chernogor ◽  
Igor Blinkov ◽  
Alexey Volkhonskiy
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Monte Carlo ◽  
Monte Carlo Calculation ◽  
Inhomogeneous Magnetic Field ◽  
Flow Energy ◽  
Wide Range ◽  
Field Concentrator ◽  
Cathodic Arc ◽  
The Magnetic Field

The flow, energy distribution and concentrations profiles of Ti ions in cathodic arc are studied by test particle Monte Carlo simulations with considering the mass transfer through the macro-particles filters with inhomogeneous magnetic field. The loss of ions due to their deposition on filter walls was calculated as a function of electric current and number of turns in the coil. The magnetic field concentrator that arises in the bending region of the filters leads to increase the loss of the ions component of cathodic arc. The ions loss up to 80 % of their energy resulted by the paired elastic collisions which correspond to the experimental results. The ion fluxes arriving at the surface of the substrates during planetary rotating of them opposite the evaporators mounted to each other at an angle of 120° characterized by the wide range of mutual overlapping.

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