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Bragg-grating solitons in a semilinear dual-core system 半线性双核系统中的布拉格光栅孤子
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8713
Atai, Malomed
{"title":"Bragg-grating solitons in a semilinear dual-core system","authors":"Atai,&nbsp;Malomed","doi":"10.1103/physreve.62.8713","DOIUrl":"https://doi.org/10.1103/physreve.62.8713","url":null,"abstract":"<p><p>We investigate the existence and stability of gap solitons in a double-core optical fiber, where one core has the Kerr nonlinearity and the other one is linear, with the Bragg grating (BG) written on the nonlinear core, while the linear one may or may not have a BG. The model considerably extends the previously studied families of BG solitons. For zero-velocity solitons, we find exact solutions in a limiting case when the group-velocity terms are absent in the equation for the linear core. In the general case, solitons are found numerically. Stability borders for the solitons are found in terms of an internal parameter of the soliton family. Depending on the frequency omega, the solitons may remain stable for large values of the group velocity in the linear core. Stable moving solitons are also found. They are produced by interaction of initially separated solitons, which shows a considerable spontaneous symmetry breaking in the case when the solitons attract each other.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8713-8"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8713","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21960258","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: 53
Extremal paths on a random cayley tree 随机凯利树的极值路径
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.7735
Majumdar, Krapivsky
{"title":"Extremal paths on a random cayley tree","authors":"Majumdar,&nbsp;Krapivsky","doi":"10.1103/physreve.62.7735","DOIUrl":"https://doi.org/10.1103/physreve.62.7735","url":null,"abstract":"<p><p>We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a distribution rho(l). Besides, the number of branches from any node is also random. Exact results are derived for arbitrary distribution rho(l). In particular, for the binary 0,1 distribution rho(l)=pdelta(l,1)+(1-p)delta(l, 0), we show that as p increases, the minimal length undergoes an unbinding transition from a \"localized\" phase to a \"moving\" phase at the critical value, p=p(c)=1-b(-1), where b is the average branch number of the tree. As the height n of the tree increases, the minimal length saturates to a finite constant in the localized phase (p<p(c)), but increases linearly as v(min)(p)n in the moving phase (p>p(c)) where the velocity v(min)(p) is determined via a front selection mechanism. At p=p(c), the minimal length grows with n in an extremely slow double-logarithmic fashion. The length of the maximal path, on the other hand, increases linearly as v(max)(p)n for all p. The maximal and minimal velocities satisfy a general duality relation, v(min)(p)+v(max)(1-p)=1, which is also valid for directed paths on finite-dimensional lattices.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt A","pages":"7735-42"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.7735","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21960672","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
Scaled structures in late stages of microphase separation of binary paraffin mixtures 二元石蜡混合物微相分离后期的尺度结构
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8234
Zhu, White, Epperson
{"title":"Scaled structures in late stages of microphase separation of binary paraffin mixtures","authors":"Zhu,&nbsp;White,&nbsp;Epperson","doi":"10.1103/physreve.62.8234","DOIUrl":"https://doi.org/10.1103/physreve.62.8234","url":null,"abstract":"<p><p>Since the dynamic properties in paraffin mixtures are different from those in alloys and polymer blends, paraffin mixtures are believed to be another class of substances establishing the \"universality\" of the dynamical scaling behavior of phase separation. In this paper, the scaled structures of microphase separation in paraffin mixtures are described using a scaling function based on a two-phase model with kinetics based on the Cahn-Hilliard equation. It has been demonstrated that at the late stages of the microphase separation the scaling behavior in the paraffin mixtures agrees well with the universal features predicted by the scaling function. The scaled structures of microphase separation in paraffin mixtures can be directly calculated from the volume fraction of the minority phase without any adjustable parameter.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8234-40"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8234","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21960680","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
Photonic hall effect in absorbing media 吸收介质中的光子霍尔效应
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8636
Wiebel, Sparenberg, Rikken, Lacoste, van Tiggelen BA
{"title":"Photonic hall effect in absorbing media","authors":"Wiebel,&nbsp;Sparenberg,&nbsp;Rikken,&nbsp;Lacoste,&nbsp;van Tiggelen BA","doi":"10.1103/physreve.62.8636","DOIUrl":"https://doi.org/10.1103/physreve.62.8636","url":null,"abstract":"<p><p>We describe an experimental and theoretical study of the effect of optical absorption on the photonic Hall effect in a passive matrix containing magnetoactive scatterers. We find that for the case of absorbing scatterers, the magnetotransverse light current changes sign and increases with increasing absorption. Good agreement is obtained with numerical calculations. For the case of an absorbing matrix, no effect was observed.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8636-9"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8636","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21961043","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: 14
Coarsening of a class of driven striped structures 一类驱动条纹构造的粗化
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.7619
Evans, Kafri, Levine, Mukamel
{"title":"Coarsening of a class of driven striped structures","authors":"Evans,&nbsp;Kafri,&nbsp;Levine,&nbsp;Mukamel","doi":"10.1103/physreve.62.7619","DOIUrl":"https://doi.org/10.1103/physreve.62.7619","url":null,"abstract":"<p><p>The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reaction-diffusion process A+A-->A to the case of extended coalescing objects, namely, the interfaces. Scaling arguments which relate the coarsening process to the evolution of a single driven interface are given, yielding growth laws for l(t), for both short and long times. We introduce a simple microscopic model for this process. Numerical simulations of the model confirm the scaling picture and growth laws. The results are compared to the case where the stripes are not driven and different growth laws arise.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt A","pages":"7619-26"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.7619","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21958989","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: 6
Invasion percolation with temperature and the nature of self-organized criticality in real systems 温度入侵渗透与实际系统自组织临界的性质
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.7638
Gabrielli, Caldarelli, Pietronero
{"title":"Invasion percolation with temperature and the nature of self-organized criticality in real systems","authors":"Gabrielli,&nbsp;Caldarelli,&nbsp;Pietronero","doi":"10.1103/physreve.62.7638","DOIUrl":"https://doi.org/10.1103/physreve.62.7638","url":null,"abstract":"<p><p>In this paper we present a theoretical approach that allows us to describe the transition between critical and noncritical behavior when stocastic noise is introduced in extremal models with disorder. Namely, we show that the introduction of thermal noise in invasion percolation (IP) brings the system outside the critical point. This result suggests a possible definition of self-organized criticality systems as ordinary critical systems where the critical point corresponds to set to 0 one of the parameters. We recover both the IP and Eden models for T-->0 and T-->infinity, respectively. For small T we find a dynamical second-order transition with correlation length diverging when T-->0.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt A","pages":"7638-41"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.7638","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21958992","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: 7
Finite-amplitude double-component convection due to different boundary conditions for two compensating horizontal gradients 两个补偿水平梯度不同边界条件下的有限振幅双分量对流
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.r7591
Tsitverblit
{"title":"Finite-amplitude double-component convection due to different boundary conditions for two compensating horizontal gradients","authors":"Tsitverblit","doi":"10.1103/physreve.62.r7591","DOIUrl":"https://doi.org/10.1103/physreve.62.r7591","url":null,"abstract":"<p><p>Finite-amplitude convective steady flows that do not bifurcate from the respective conduction state are discovered. They arise as the compensating horizontal gradients of two density-affecting components with equal diffusivities but different boundary conditions are applied to the Boussinesq fluid at rest with and without stable vertical stratification. These flows emanate from convection in a laterally heated stably stratified slot. Their relevance to convective states in a horizontal slot with two vertical gradients, emphasizing universality of the underlying type of convection, is discussed.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt A","pages":"R7591-4"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.r7591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21959006","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: 2
High-precision, variational, bound-state calculations in coulomb three-body systems 库仑三体系统的高精度变分束缚态计算
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8740
Frolov
{"title":"High-precision, variational, bound-state calculations in coulomb three-body systems","authors":"Frolov","doi":"10.1103/physreve.62.8740","DOIUrl":"https://doi.org/10.1103/physreve.62.8740","url":null,"abstract":"<p><p>The present study contains high-precision variational results for a number of bound states in various Coulomb three-body systems. In particular, we discuss the bound-state properties for the 2(3)S state of the infinityHe atom, the bound S(L=0) and P(L=1) states in symmetric muonic molecular ions, and ground states in the 3He2+&mgr;(-)e(-) and 4He2+&mgr;(-)e(-) atoms. The accuracy achieved for the total energies in these systems is significantly higher than known from the previous works. These results have been obtained by using a package of FORTRAN programs and a pretranslator written by D. H. Bailey from NASA [D.H. Bailey, ACM Trans. Math. Softw. 21, 379 (1995)]. This multiprecision FORTRAN package can completely eliminate all problems related to numerical instabilities at large dimensions, which are crucial for high-precision, bound-state calculations in few-body systems. In fact, the multiprecision FORTRAN programs open another avenue in the study of bound states in few-body systems.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8740-5"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8740","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21959008","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: 11
Fourier grid hamiltonian method and lagrange-mesh calculations 傅里叶网格哈密顿方法和拉格朗日网格计算
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8777
Semay
{"title":"Fourier grid hamiltonian method and lagrange-mesh calculations","authors":"Semay","doi":"10.1103/physreve.62.8777","DOIUrl":"https://doi.org/10.1103/physreve.62.8777","url":null,"abstract":"<p><p>Bound state eigenvalues and eigenfunctions of a Schrodinger equation or a spinless Salpeter equation can be simply and accurately computed by the Fourier grid Hamiltonian (FGH) method. It requires only the evaluation of the potential at equally spaced grid points, and yields the eigenfunctions at the same grid points. The Lagrange-mesh (LM) method is another simple procedure to solve a Schrodinger equation on a mesh. It is shown that the FGH method is a special case of a LM calculation in which the kinetic energy operator is treated by a discrete Fourier transformation. This gives a firm basis for the FGH method and makes possible the evaluation of the eigenfunctions obtained with this method at any arbitrary values.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8777-81"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21959013","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
Optimal pruning in neural networks. 神经网络中的最优修剪。
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Pub Date : 2000-12-01 DOI: 10.1103/physreve.62.8387
D M Barbato, O Kinouchi
{"title":"Optimal pruning in neural networks.","authors":"D M Barbato,&nbsp;O Kinouchi","doi":"10.1103/physreve.62.8387","DOIUrl":"https://doi.org/10.1103/physreve.62.8387","url":null,"abstract":"<p><p>We study pruning strategies in simple perceptrons subjected to supervised learning. Our analytical results, obtained through the statistical mechanics approach to learning theory, are independent of the learning algorithm used in the training process. We calculate the post-training distribution P(J) of synaptic weights, which depends only on the overlap rho(0) achieved by the learning algorithm before pruning and the fraction kappa of relevant weights in the teacher network. From this distribution, we calculate the optimal pruning strategy for deleting small weights. The optimal pruning threshold grows from zero as straight theta(opt)(rho(0), kappa) approximately [rho(0)-rho(c)(kappa)](1/2) above some critical value rho(c)(kappa). Thus, the elimination of weak synapses enhances the network performance only after a critical learning period. Possible implications for biological pruning phenomena are discussed.</p>","PeriodicalId":20079,"journal":{"name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","volume":"62 6 Pt B","pages":"8387-94"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1103/physreve.62.8387","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21959301","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: 11
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