scholarly journals GEOMETRIC LANGEVIN EQUATIONS ON SUBMANIFOLDS AND APPLICATIONS TO THE STOCHASTIC MELT-SPINNING PROCESS OF NONWOVENS AND BIOLOGY

2013 ◽  
Vol 13 (04) ◽  
pp. 1350001 ◽  
Author(s):  
MARTIN GROTHAUS ◽  
PATRIK STILGENBAUER
Keyword(s):  
Euclidean Space ◽  
Mathematical Models ◽  
Langevin Equation ◽  
Melt Spinning ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Langevin Equations ◽  
Spinning Process ◽  
Differential Equations On Manifolds ◽  
Natural Way

In this paper we develop geometric versions of the classical Langevin equation on regular submanifolds in Euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Lelièvre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant Euclidean norm. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jørgensen or Kolokoltsov. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We light up the geometry occurring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. Finally, relations to a class of swarming models are presented and further applications of the geometric Langevin equations are given.

Modeling and Optimization of Nozzle Design in Planar Flow Melt Spinning

1999 ◽  
Author(s):  
J. S.-J. Chen ◽  
A. A. Tseng
Keyword(s):  
Melt Spinning ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Cfd Modeling ◽  
Nozzle Design ◽  
Planar Flow ◽  
Injection Angle ◽  
Image Velocimetry ◽  
Spinning Process

Abstract Numerical and experimental studies were performed to analyze a planar flow melt spinning process (PFMS) with a focus on the optimal nozzle design. Three-dimensional computational fluid dynamics (CFD) modeling using FIDAP was carried out to analyze the flow distribution in various nozzle shapes including rectangular, trapezoidal, and hemispherical edges. A laser-based Particle Image Velocimetry (PIV) system was developed to measure the velocity field at the nozzle exit. The CFD modeling results were validated by the PIV measurements. It was found that a converging nozzle with diverging edges along with a 30°-injection angle provided the best design. The optimized nozzle was used to produce high quality ribbons as characterized by the surface roughness measurements and micrograph techniques.

scholarly journals Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

2021 ◽  
Author(s):  
Adrien Laurent ◽  
Gilles Vilmart
Keyword(s):  
Invariant Measure ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Group ◽  
Langevin Equation ◽  
Numerical Experiments ◽  
Special Linear Group ◽  
Order Conditions ◽  
High Order ◽  
Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

scholarly journals A computer-based approach for developing linamarase inhibitory agents

2020 ◽  
Vol 5 (7) ◽  
Author(s):  
Lucas Paul ◽  
Celestin N. Mudogo ◽  
Kelvin M. Mtei ◽  
Revocatus L. Machunda ◽  
Fidele Ntie-Kang
Keyword(s):  
Structure Elucidation ◽  
Three Dimensional ◽  
Data Bank ◽  
Competitive Inhibitor ◽  
Industrial Applications ◽  
Dimensional Structure ◽  
Full Understanding ◽  
The Poor ◽  
Computer Based ◽  
Inhibitory Agents

AbstractCassava is a strategic crop, especially for developing countries. However, the presence of cyanogenic compounds in cassava products limits the proper nutrients utilization. Due to the poor availability of structure discovery and elucidation in the Protein Data Bank is limiting the full understanding of the enzyme, how to inhibit it and applications in different fields. There is a need to solve the three-dimensional structure (3-D) of linamarase from cassava. The structural elucidation will allow the development of a competitive inhibitor and various industrial applications of the enzyme. The goal of this review is to summarize and present the available 3-D modeling structure of linamarase enzyme using different computational strategies. This approach could help in determining the structure of linamarase and later guide the structure elucidation in silico and experimentally.

scholarly journals Enhanced catalytic ozonation of ibuprofen using a 3D structured catalyst with MnO2 nanosheets on carbon microfibers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guhankumar Ponnusamy ◽  
Hajar Farzaneh ◽  
Yongfeng Tong ◽  
Jenny Lawler ◽  
Zhaoyang Liu ◽  
...  
Keyword(s):  
Removal Efficiency ◽  
Active Sites ◽  
Low Cost ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Catalytic Ozonation ◽  
Heterogeneous Catalytic ◽  
Structured Catalyst ◽  
Dimensional Network ◽  
Carbon Microfibers

AbstractHeterogeneous catalytic ozonation is an effective approach to degrade refractory organic pollutants in water. However, ozonation catalysts with combined merits of high activity, good reusability and low cost for practical industrial applications are still rare. This study aims to develop an efficient, stable and economic ozonation catalyst for the degradation of Ibuprofen, a pharmaceutical compound frequently detected as a refractory pollutant in treated wastewaters. The novel three-dimensional network-structured catalyst, comprising of δ-MnO2 nanosheets grown on woven carbon microfibers (MnO2 nanosheets/carbon microfiber), was synthesized via a facile hydrothermal approach. Catalytic ozonation performance of Ibuprofen removal in water using the new catalyst proves a significant enhancement, where Ibuprofen removal efficiency of close to 90% was achieved with a catalyst loading of 1% (w/v). In contrast, conventional ozonation was only able to achieve 65% removal efficiency under the same operating condition. The enhanced performance with the new catalyst could be attributed to its significantly increased available surface active sites and improved mass transfer of reaction media, as a result of the special surface and structure properties of this new three-dimensional network-structured catalyst. Moreover, the new catalyst displays excellent stability and reusability for ibuprofen degradation over successive reaction cycles. The facile synthesis method and low-cost materials render the new catalyst high potential for industrial scaling up. With the combined advantages of high efficiency, high stability, and low cost, this study sheds new light for industrial applications of ozonation catalysts.

scholarly journals Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180131 ◽  
Author(s):  
Luca Giuggioli ◽  
Zohar Neu
Keyword(s):  
Langevin Equation ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Delay Systems ◽  
Langevin Equations ◽  
Delayed Systems ◽  
Temporal Features ◽  
Fokker Planck Equations ◽  
Random Fluctuations ◽  
Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n  = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

Effect of Crucible Parameters on Planar Flow Melt Spinning Process

2015 ◽  
Vol 68 (6) ◽  
pp. 1125-1129 ◽  
Author(s):  
M. Swaroopa ◽  
L. Venu Gopal ◽  
T. Kishen Kumar Reddy ◽  
B. Majumdar
Keyword(s):  
Melt Spinning ◽  
Planar Flow ◽  
Spinning Process

scholarly journals On a Question of Bourgain about Geometric Incidences

2008 ◽  
Vol 17 (4) ◽  
pp. 619-625 ◽  
Author(s):  
JÓZSEF SOLYMOSI ◽  
CSABA D. TÓTH
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Geometric Incidences

Given a set of s points and a set of n2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, we show that s = Ω(n11/4). This is the first non-trivial answer to a question recently posed by Jean Bourgain.

scholarly journals Orthogonal Isomorphic Representations Of Free Groups

1956 ◽  
Vol 8 ◽  
pp. 256-262 ◽  
Author(s):  
J. De Groot
Keyword(s):  
Euclidean Space ◽  
Free Groups ◽  
Three Dimensional ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Orthogonal Matrices ◽  
Abelian Subgroups ◽  
Proper Orthogonal

1. Introduction. We consider the group of proper orthogonal transformations (rotations) in three-dimensional Euclidean space, represented by real orthogonal matrices (aik) (i, k = 1,2,3) with determinant + 1 . It is known that this rotation group contains free (non-abelian) subgroups; in fact Hausdorff (5) showed how to find two rotations P and Q generating a group with only two non-trivial relationsP2 = Q3 = I.

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