scholarly journals Monte Carlo computer investigations of higher generation ideal dendrimers

2021 ◽  
Vol 24 (2) ◽  
pp. 23301
Author(s):  
M. Jura ◽  
M. Bishop ◽  
B. Thrope ◽  
R. de Regt
Keyword(s):  
Monte Carlo ◽  
Graph Representation ◽  
Radius Of Gyration ◽  
Theory Approach ◽  
Shape Parameters ◽  
Novel Technique ◽  
Theoretical Predictions ◽  
The Mean ◽  
Kirchhoff Matrix ◽  
Number Of Branches

The properties of ideal tri-functional dendrimers with forty-five, ninety-three and one hundred and eighty-nine branches are investigated. Three methods are employed to calculate the mean-square radius of gyration, g-ratios, asphericity, shape parameters and form factor. These methods include a Kirchhoff matrix eigenvalue technique, the graph theory approach of Benhamou et al. (2004), and Monte Carlo simulations using a growth algorithm. A novel technique for counting paths in the graph representation of the dendrimers is presented. All the methods are in excellent agreement with each other and with available theoretical predictions. Dendrimers become more symmetrical as the generation and the number of branches increase.

Monte Carlo Simulation on Conformation Properties of Polymer Multiple Chain System

2013 ◽  
Vol 734-737 ◽  
pp. 3141-3144
Author(s):  
Lin Lin Cui ◽  
Hua Nan Guan
Keyword(s):  
Monte Carlo ◽  
Polymer Chain ◽  
Volume Fraction ◽  
Solvent Molecule ◽  
Radius Of Gyration ◽  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
Multiple Chain ◽  
Linear Polymer Chain

The author adopts Monte Carlo compute method to simulate the linear polymer chain lattice model in multiple chain systems of different volume fraction Φ while chain lengthn=50, and makes a research on the variational situation of the size (measured with the mean-square end-to-end distance <R2> and the mean-square radius of gyration <S2>), shape (measured with the mean asphericity factor ) with changing of the interaction energy between solvent molecule and polymer chain segment moleculeεPS. Results indicate <R2>, <S2> and have the changing rules that they become small with the increase of theεPS.

scholarly journals CRUMPLED-TO-TUBULE TRANSITION AND SHAPE TRANSFORMATIONS OF A MODEL OF SELF-AVOIDING SPHERICAL MESHWORK

2013 ◽  
Vol 24 (10) ◽  
pp. 1350075
Author(s):  
HIROSHI KOIBUCHI ◽  
ANDREY SHOBUKHOV
Keyword(s):  
Monte Carlo ◽  
Fractal Dimension ◽  
Pressure Difference ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Pressure Term ◽  
Second Order Transition ◽  
The Mean ◽  
Mc Simulation ◽  
The One

This paper analyzes a new self-avoiding (SA) meshwork model using the canonical Monte Carlo (MC) simulation technique on lattices that consist of connection-fixed triangles. The Hamiltonian of this model includes a SA potential and a pressure term. The model identifies a crumpled-to-tubule (CT) transition between the crumpled and tubular phases. This is a second-order transition, which occurs when the pressure difference between the inner and outer sides of the surface is close to zero. We obtain the Flory swelling exponents [Formula: see text] and [Formula: see text] corresponding to the mean square radius of gyration [Formula: see text] and enclosed volume V, where Df is the fractal dimension. The analysis shows that [Formula: see text] at the transition is almost identical to the one of the smooth phase of previously reported SA model which has no crumpled phase.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

Kinetic Monte Carlo Simulation of Impurity Effects on Nucleation and Growth of SiC Clusters on Si(100)

2013 ◽  
Vol 740-742 ◽  
pp. 393-396
Author(s):  
Maxim N. Lubov ◽  
Jörg Pezoldt ◽  
Yuri V. Trushin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Cluster Size ◽  
Kinetic Monte Carlo ◽  
Nucleation And Growth ◽  
Nucleation Density ◽  
Nucleation Process ◽  
Impurity Effects ◽  
Kinetic Monte Carlo Simulations ◽  
The Mean

The influence of attractive and repulsive impurities on the nucleation process of the SiC clusters on Si(100) surface was investigated. Kinetic Monte Carlo simulations of the SiC clusters growth show that that increase of the impurity concentration (both attractive and repulsive) leads to decrease of the mean cluster size and rise of the nucleation density of the clusters.

scholarly journals Evaluation of Bearing Capacity of Strip Footing Using Random Layers Concept

2015 ◽  
Vol 37 (3) ◽  
pp. 31-39 ◽  
Author(s):  
Marek Kawa ◽  
Dariusz Łydżba
Keyword(s):  
Monte Carlo ◽  
Bearing Capacity ◽  
Failure Mechanism ◽  
Design Theory ◽  
Cohesive Soil ◽  
Probability Of Failure ◽  
Mean Value ◽  
Strip Footing ◽  
Random Field Theory ◽  
The Mean

Abstract The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

A numerical study of the sedimentation of fibre suspensions

1998 ◽  
Vol 376 ◽  
pp. 149-182 ◽  
Author(s):  
MICHAEL B. MACKAPLOW ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Numerical Study ◽  
Point Particle ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Fibre Suspensions ◽  
The Mean

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

Jupiter's Zonal Vorticity Profile Observed by JunoCam

2021 ◽  
Author(s):  
Gerald Eichstädt ◽  
John Rogers ◽  
Glenn Orton ◽  
Candice Hansen
Keyword(s):  
Monte Carlo ◽  
Wind Profile ◽  
Image Pair ◽  
Stereo Correspondence ◽  
Cyclonic Vorticity ◽  
Latitude Range ◽  
Novel Structure ◽  
The Mean ◽  
Image Pairs ◽  
Cloud Tops

&lt;p&gt;We derive Jupiter's zonal vorticity profile from JunoCam images, with Juno's polar orbit allowing the observation of latitudes that are difficult to observe from Earth or from equatorial flybys. &amp;#160;We identify cyclonic local vorticity maxima near 77.9&amp;#176;, 65.6&amp;#176;, 59.3&amp;#176;, 50.9&amp;#176;, 42.4&amp;#176;, and 34.3&amp;#176;S planetocentric at a resolution of ~1&amp;#176;, based on analyzing selected JunoCam image pairs taken during the 16 Juno perijove flybys 15-30. We identify zonal anticyclonic local vorticity maxima near 80.7&amp;#176;, 73.8&amp;#176;, 62.1&amp;#176;, 56.4&amp;#176;, 46.9&amp;#176;, 38.0&amp;#176;, and 30.7&amp;#176;S. &amp;#160;These results agree with the known zonal wind profile below 64&amp;#176;S, and reveal novel structure further south, including a prominent cyclonic band centered near 66&amp;#176;S. The anticyclonic vorticity maximum near 73.8&amp;#176;S represents a broad and skewed fluctuating anticyclonic band between ~69.0&amp;#176; and ~76.5&amp;#176;S, and is hence poorly defined. This band may even split temporarily into two or three bands. &amp;#160;The cyclonic vorticity maximum near 77.9&amp;#176;S appears to be fairly stable during these flybys, probably representing irregular cyclonic structures in the region. The area between ~82&amp;#176; and 90&amp;#176;S is relatively small and close to the terminator, resulting in poor statistics, but generally shows a strongly cyclonic mean vorticity, representing the well-known circumpolar cyclone cluster.&lt;/p&gt;&lt;p&gt;The latitude range between ~30&amp;#176;S and ~85&amp;#176;S was particularly well observed, allowing observation periods lasting several hours. For each considered perijove we selected a pair of images separated by about 30 - 60 minutes. We derived high-passed and contrast-normalized south polar equidistant azimuthal maps of Jupiter's cloud tops. They were used to derive maps of local rotation at a resolution of ~1&amp;#176; latitude by stereo-corresponding Monte-Carlo-distributed and Gauss-weighted round tiles for each image pair considered. Only the rotation portion of the stereo correspondence between tiles was used to sample the vorticity maps. For each image pair, we rendered ~40 vorticity maps with different Monte-Carlo runs. The standard deviation of the resulting statistics provided a criterion to define a valid area of the mean vorticity map. Averaging vorticities along circles centered on the south pole returned a zonal vorticity profile for each of the perijoves considered. Averaging the resulting zonal vorticity profiles built the basis for a discussion of the mean profile.&lt;/p&gt;&lt;p&gt;JunoCam also images the northern hemisphere, at higher resolution but with coverage restricted to a briefer time span and smaller area due to the nature of Juno's elliptical orbit, which will restrict our ability to obtain zonal vorticity profiles.&lt;/p&gt;

An Experimental Investigation of Flow-Induced Cavity Resonance

2001 ◽  
Author(s):  
Paul J. Zoccola ◽  
Theodore M. Farabee
Keyword(s):  
Experimental Investigation ◽  
Energy Production ◽  
Pressure Fluctuations ◽  
Cavity Resonance ◽  
Cavity Pressure ◽  
Novel Technique ◽  
Cavity Opening ◽  
The Mean ◽  
Marine Applications ◽  
Opening Phase

Abstract Excitation of cavity resonance by flow over an aperture is often a source of unwanted noise in aerospace, automotive, and marine applications. An experimental investigation of this phenomenon was conducted. Detailed measurements of the cavity pressure and the velocity field in the opening were performed in a quiet flow facility. Spectral data on cavity pressure fluctuations obtained for a variety of configurations were analyzed over a range of speeds to determine the behavior of both sheartones and cavity tones during non-resonant and resonant conditions. The mean and fluctuating velocity profiles as well as the cross-spectral properties between the velocity components and cavity pressure were also obtained within the cavity opening. Phase between the velocity components and the pressure was used to calculate the streamwise convection velocities across the opening. A novel technique used to measure vorticity allowed calculation of the measured energy production in the opening. The data support the finding that the resonant and non-resonant conditions are distinguished by the behavior of the convection velocity and by the distribution of energy production in the flow field.

scholarly journals Modeling Replenishment of Ultrathin Liquid Perfluoropolyether Z Films on Solid Surfaces Using Monte Carlo Simulation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
M. S. Mayeed ◽  
T. Kato
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Liquid Films ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Carbon Surface ◽  
Radius Of Gyration ◽  
Constant Multiple ◽  
Molecular Weights ◽  
Lattice Polymer

Applying the reptation algorithm to a simplified perfluoropolyether Z off-lattice polymer model an NVT Monte Carlo simulation has been performed. Bulk condition has been simulated first to compare the average radius of gyration with the bulk experimental results. Then the model is tested for its ability to describe dynamics. After this, it is applied to observe the replenishment of nanoscale ultrathin liquid films on solid flat carbon surfaces. The replenishment rate for trenches of different widths (8, 12, and 16 nms for several molecular weights) between two films of perfluoropolyether Z from the Monte Carlo simulation is compared to that obtained solving the diffusion equation using the experimental diffusion coefficients of Ma et al. (1999), with room condition in both cases. Replenishment per Monte Carlo cycle seems to be a constant multiple of replenishment per second at least up to 2 nm replenished film thickness of the trenches over the carbon surface. Considerable good agreement has been achieved here between the experimental results and the dynamics of molecules using reptation moves in the ultrathin liquid films on solid surfaces.

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