scholarly journals Analytical solution for time integrals in diagrammatic expansions: Application to real-frequency diagrammatic Monte Carlo

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
J. Vučičević ◽  
P. Stipsić ◽  
M. Ferrero
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Real Frequency

A Solar Trough Concentrator for Pill-Box Flux Distribution Over a CPV Panel

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
R. Bader ◽  
A. Steinfeld
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Ray Tracing ◽  
Focal Plane ◽  
Flux Distribution ◽  
Solar Flux ◽  
Target Area ◽  
Mirror Surface ◽  
Surface Imperfections ◽  
Flux Concentration

An integral methodology is formulated to analytically derive the exact profile of a solar trough concentrator that delivers a uniform radiative flux distribution over a flat rectangular target area at the focal plane. The Monte Carlo ray-tracing technique is applied to verify the analytical solution and investigate the effect of sun shape and mirror surface imperfections on the radiation uniformity and spillage. This design is pertinent to concentrating photovoltaics at moderate mean solar flux concentration ratios of up to 50 suns.

Lidar returns from multiply scattering media in multiple-field-of-view and CCD lidars with polarization devices: comparison of semi-analytical solution and Monte Carlo data

2009 ◽  
Vol 48 (3) ◽  
pp. 623 ◽  
Author(s):  
Ludmila I. Chaikovskaya ◽  
Eleonora P. Zege ◽  
Iosif L. Katsev ◽  
Markus Hirschberger ◽  
Ulrich G. Oppel
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Field Of View ◽  
Scattering Media ◽  
Monte Carlo Data ◽  
Multiple Field

scholarly journals Analytical solution of the Monte Carlo dynamics of a simple spin-glass model

1996 ◽  
Vol 34 (3) ◽  
pp. 159-164 ◽  
Author(s):  
L. L Bonilla ◽  
F. G Padilla ◽  
G Parisi ◽  
F Ritort
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Spin Glass ◽  
Spin Glass Model ◽  
Glass Model ◽  
Monte Carlo Dynamics

scholarly journals Pricing the exotic: Path-dependent American options with stochastic barriers

2021 ◽  
Author(s):  
Alejandro Rojas-Bernal ◽  
Mauricio Villamizar-Villegas
Keyword(s):  
Risk Factors ◽  
Monte Carlo ◽  
Analytical Solution ◽  
American Options ◽  
Pricing Strategy ◽  
Computational Time ◽  
European Options ◽  
Standard Methods ◽  
Path Dependent ◽  
Closed Form Approximation

We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.

scholarly journals A memory-based random walk model to understand diffusion in crowded heterogeneous environment

2018 ◽  
Vol 32 (16) ◽  
pp. 1850193
Author(s):  
Sabeeha Hasnain ◽  
Upendra Harbola ◽  
Pradipta Bandyopadhyay
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Analytical Solution ◽  
Heterogeneous Environments ◽  
Time Behavior ◽  
Heterogeneous Environment ◽  
Long Time Behavior ◽  
Current Time ◽  
Long Time ◽  
Mc Simulation

We study memory-based random walk models to understand diffusive motion in crowded heterogeneous environments. The models considered are non-Markovian as the current move of the random walk is determined by randomly selecting a move from history. At each step, particle can take right, left or stay moves which is correlated with the randomly selected past step. There is a perfect stay–stay correlation which ensures that the particle does not move if the randomly selected past step is a stay move. The probability of traversing the same direction as the chosen history or reversing it depends on the current time and the time or position of the history selected. The time- or position-dependent biasing in moves implicitly corresponds to the heterogeneity of the environment and dictates the long-time behavior of the dynamics that can be diffusive, sub or superdiffusive. A combination of analytical solution and Monte Carlo (MC) simulation of different random walk models gives rich insight on the effects of correlations on the dynamics of a system in heterogeneous environment.

scholarly journals Monte Carlo Simulation of Stochastic Adsorption of Diluted Solute Molecules at an Interface

2020 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Observation Time ◽  
Patterned Surfaces ◽  
Fractal Function ◽  
Self Assembled Monolayer ◽  
Power Law Decay ◽  
Sensing Platforms ◽  
Surface Collision ◽  
Measuring Frequency

<div> <p>Here an analytical solution of Fick’s 2<sup>nd</sup> law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

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