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arXiv: Pattern Formation and Solitons最新文献

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Mapping Between Nonlinear Sch"odinger Equations with Real and Complex Potentials 具有实势和复势的非线性schodinger方程的映射
arXiv: Pattern Formation and Solitons Pub Date : 2013-06-16 DOI: 10.7546/jgsp-32-2013-25-35
M. Salerno
{"title":"Mapping Between Nonlinear Sch\"odinger Equations with Real and Complex Potentials","authors":"M. Salerno","doi":"10.7546/jgsp-32-2013-25-35","DOIUrl":"https://doi.org/10.7546/jgsp-32-2013-25-35","url":null,"abstract":"A mapping between stationary solutions of nonlinear Sch\"odinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific examples we consider the case of the damped dynamics of a quantum harmonic oscillator and the case of dissipative periodic soliton solutions of the nonlinear Schr\"odinger equation with complex potential.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130087199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Stability of Mode-Locked Kinks in the AC Driven and Damped Sine-Gordon Lattice 交流驱动和阻尼正弦戈登晶格中锁模扭结的稳定性
arXiv: Pattern Formation and Solitons Pub Date : 2013-06-11 DOI: 10.1007/978-3-319-02057-0_12
Y. Zolotaryuk
{"title":"Stability of Mode-Locked Kinks in the AC Driven and Damped Sine-Gordon Lattice","authors":"Y. Zolotaryuk","doi":"10.1007/978-3-319-02057-0_12","DOIUrl":"https://doi.org/10.1007/978-3-319-02057-0_12","url":null,"abstract":"","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126656222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatial pattern of discrete and ultradiscrete Gray-Scott model 离散和超离散Gray-Scott模型的空间格局
arXiv: Pattern Formation and Solitons Pub Date : 2013-05-23 DOI: 10.3934/DCDSB.2015.20.173
K. Matsuya, M. Murata
{"title":"Spatial pattern of discrete and ultradiscrete Gray-Scott model","authors":"K. Matsuya, M. Murata","doi":"10.3934/DCDSB.2015.20.173","DOIUrl":"https://doi.org/10.3934/DCDSB.2015.20.173","url":null,"abstract":"Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure preserves the essential properties of the original equation, such as the structure of exact solutions for integrable equations. In this article, we propose a discretization and an ultradiscretization of Gray-Scott model which is not an integrable system and which gives various spatial patterns with appropriate initial data and parameters. The resulting systems give a travelling pulse and a self-replication pattern with appropriate initial data and parameters. The ultradiscrete system is directly related to the elementary cellular automaton Rule 90 which gives a Sierpinski gasket pattern. A $(2+1)$D ultradiscrete Gray-Scott model that gives a ring pattern, a self-replication pattern and a chaotic pattern, is also constructed.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"363 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125702252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
The effect of tow gaps on compression after impact strength of robotically laminated structures 两个间隙对机器人层合结构冲击后压缩强度的影响
arXiv: Pattern Formation and Solitons Pub Date : 2013-05-01 DOI: 10.3970/CMC.2013.035.001
A. Rhead, T. Dodwell, R. Butler
{"title":"The effect of tow gaps on compression after impact strength of robotically laminated structures","authors":"A. Rhead, T. Dodwell, R. Butler","doi":"10.3970/CMC.2013.035.001","DOIUrl":"https://doi.org/10.3970/CMC.2013.035.001","url":null,"abstract":"When (robotic) Automated Fibre Placement (AFP) is used to manufacture aerospace components with complex three dimensional geometries, gaps between fibre tows can occur. This paper is the first to explore the interaction under compressive load of these tow gaps with impact damage. Two coupons with different distributions of tow-gaps were impacted. Results indicated that the area of delamination is smaller for an impact directly over a tow gap where the tow gap is situated close to the non-impact face. Subsequent Compression After Impact (CAI) testing demonstrated that both the formation of sublaminate buckles and subsequent growth of delaminations is inhibited by the presence of a tow gap near the non-impact face. Non-destructive testing techniques and a computationally efficient infinite Strip model are used to analyse the damage resistance and damage tolerance of the coupons. A new validation of the Strip model is also presented.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"293 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125729638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
On blowup dynamics in the Keller-Segel model of chemotaxis 趋化性Keller-Segel模型的爆破动力学
arXiv: Pattern Formation and Solitons Pub Date : 2013-04-04 DOI: 10.1090/S1061-0022-2014-01306-4
S. Dejak, D. Egli, P. Lushnikov, I. Sigal
{"title":"On blowup dynamics in the Keller-Segel model of chemotaxis","authors":"S. Dejak, D. Egli, P. Lushnikov, I. Sigal","doi":"10.1090/S1061-0022-2014-01306-4","DOIUrl":"https://doi.org/10.1090/S1061-0022-2014-01306-4","url":null,"abstract":"We investigate the (reduced) Keller-Segel equations modeling chemotaxis of bio-organisms. We present a formal derivation and partial rigorous results of the blowup dynamics of solution of these equations describing the chemotactic aggregation of the organisms. Our results are confirmed by numerical simulations and the formula we derive coincides with the formula of Herrero and Vel'{a}zquez for specially constructed solutions.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126657768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices 强非线性格的导阶拟连续统逼近的证明
arXiv: Pattern Formation and Solitons Pub Date : 2013-03-22 DOI: 10.3934/DCDS.2014.34.3403
C. Chong, P. Kevrekidis, G. Schneider
{"title":"Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices","authors":"C. Chong, P. Kevrekidis, G. Schneider","doi":"10.3934/DCDS.2014.34.3403","DOIUrl":"https://doi.org/10.3934/DCDS.2014.34.3403","url":null,"abstract":"We consider the leading order quasicontinuum limits of a one-dimensional granular medium governed by the Hertz contact law under precompression. The approximate model which is derived in this limit is justified by establishing asymptotic bounds for the error with the help of energy estimates. The continuum model predicts the development of shock waves, which are also studied in the full system with the aid of numerical simulations. We also show that existing results concerning the Nonlinear Schrodinger (NLS) and Korteweg de-Vries (KdV) approximation of FPU models apply directly to a precompressed granular medium in the weakly nonlinear regime.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114194882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Waves in Honeycomb Structures 蜂窝结构中的波
arXiv: Pattern Formation and Solitons Pub Date : 2012-12-30 DOI: 10.5802/JEDP.95
C. Fefferman, M. Weinstein
{"title":"Waves in Honeycomb Structures","authors":"C. Fefferman, M. Weinstein","doi":"10.5802/JEDP.95","DOIUrl":"https://doi.org/10.5802/JEDP.95","url":null,"abstract":"We review recent work of the authors on the non-relativistic Schr\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-Delta+V$ and (ii) the two-dimensional Dirac equations, as a large, but finite time, effective description of $e^{-iH_Vt}psi_0$, for data $psi_0$, which is spectrally localized at a Dirac point. We conclude with a formal derivation and discussion of the effective large time evolution for the nonlinear Schr\"odinger - Gross Pitaevskii equation for small amplitude initial conditions, $psi_0$. The effective dynamics are governed by a nonlinear Dirac system.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128379378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows 非定常胞体流动中g方程模型的湍流火焰速度
arXiv: Pattern Formation and Solitons Pub Date : 2012-10-05 DOI: 10.1051/MMNP/20138312
Yu-Yu Liu, J. Xin, Yifeng Yu
{"title":"Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows","authors":"Yu-Yu Liu, J. Xin, Yifeng Yu","doi":"10.1051/MMNP/20138312","DOIUrl":"https://doi.org/10.1051/MMNP/20138312","url":null,"abstract":"We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain G equations are also non-convex with degenerate diffusion. The computation is based on monotone finite difference discretization and weighted essentially nonoscillatory (WENO) methods. We found that the large time front speeds lock into the frequency of time periodic cellular flows in curvature-strain G-equations similar to what occurs in the basic inviscid G-equation. However, such frequency locking phenomenon disappears in viscous G-equation, and in the inviscid G-equation if time periodic oscillation of the cellular flow is replaced by time stochastic oscillation.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123461794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities 非线性离焦pt对称系统中的孤子及其鬼影
arXiv: Pattern Formation and Solitons Pub Date : 2012-08-12 DOI: 10.1007/978-3-319-02057-0_1
V. Achilleos, P. G.Kevrekidis, D. Frantzeskakis, R. Carretero-González
{"title":"Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities","authors":"V. Achilleos, P. G.Kevrekidis, D. Frantzeskakis, R. Carretero-González","doi":"10.1007/978-3-319-02057-0_1","DOIUrl":"https://doi.org/10.1007/978-3-319-02057-0_1","url":null,"abstract":"","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122028505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Symmetric and asymmetric solitons in a nonlocal nonlinear coupler 非局部非线性耦合器中的对称和非对称孤子
arXiv: Pattern Formation and Solitons Pub Date : 2012-05-17 DOI: 10.1103/PHYSREVA.85.053839
Xianling Shi, B. Malomed, F. Ye, Xianfeng Chen
{"title":"Symmetric and asymmetric solitons in a nonlocal nonlinear coupler","authors":"Xianling Shi, B. Malomed, F. Ye, Xianfeng Chen","doi":"10.1103/PHYSREVA.85.053839","DOIUrl":"https://doi.org/10.1103/PHYSREVA.85.053839","url":null,"abstract":"We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveg- uide with nonlocal (thermal) nonlinearity. In comparison with the well-known coupled systems with the local nonlinearity, the present setting is affected by the competition of different spatial scales, viz., the coupling length and correlation radius of the nonlocality, $sqrt{d}$. By means of numer- ical methods and variational approximation (VA, which is relevant for small d), we find that, with the increase of the correlation radius, the SBB changes from subcritical into supercritical, which makes all the asymmetric solitons stable. On the other hand, the nonlocality has little influence on the stability of antisymmetric solitons. Analytical results for the SBB are also obtained (actually, for antisymmetric \"accessible solitons\") in the opposite limit of the ultra-nonlocal nonlinearity, using a coupler based on the Snyder-Mitchell model. The results help to grasp the general picture of the symmetry breaking in nonlocal couplers.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115160508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
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