IMA Journal of Applied Mathematics最新文献_第7页

Laplace–Beltrami spectrum of ellipsoids that are close to spheres and analytic perturbation theory 接近球体的椭球体的拉普拉斯-贝尔特拉米谱与解析微扰理论

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-10-01 DOI: 10.1093/imamat/hxab045

Suresh Eswarathasan;Theodore Kolokolnikov

引用次数: 5

Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions 意见动力学的噪声有界置信模型：边界条件对相变的影响

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-10-01 DOI: 10.1093/imamat/hxab044

B D Goddard;B Gooding;H Short;G A Pavliotis

引用次数: 0

Dynamical aspects of a restricted three-vortex problem 一个受限三涡问题的动力学方面

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-10-01 DOI: 10.1093/imamat/hxab043

Sreethin Sreedharan Kallyadan;Priyanka Shukla

引用次数: 2

Accelerated Dirichlet–Robin alternating algorithms for solving the Cauchy problem for the Helmholtz equation 求解亥姆霍兹方程柯西问题的加速Dirichlet–Robin交替算法

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-02 DOI: 10.1093/IMAMAT/HXAB034

F. Berntsson, Jennifer Chepkorir, V. Kozlov

引用次数: 1

Snaking bifurcations of localized patterns on ring lattices 环格上局部化模式的Snaking分岔

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab023

Moyi Tian;Jason J Bramburger;Björn Sandstede

引用次数: 5

Localized states in passive and active phase-field-crystal models 被动和主动相场晶体模型中的局域态

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab025

Max Philipp Holl;Andrew J Archer;Svetlana V Gurevich;Edgar Knobloch;Lukas Ophaus;Uwe Thiele

{"title":"Localized states in passive and active phase-field-crystal models","authors":"Max Philipp Holl;Andrew J Archer;Svetlana V Gurevich;Edgar Knobloch;Lukas Ophaus;Uwe Thiele","doi":"10.1093/imamat/hxab025","DOIUrl":"10.1093/imamat/hxab025","url":null,"abstract":"The passive conserved Swift–Hohenberg equation (or phase-field-crystal [PFC] model) describes gradient dynamics of a single-order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC models with common gradient dynamics, (ii) two coupled passive PFC models where the coupling breaks the gradient dynamics structure and (iii) a passive PFC model coupled to an active PFC model.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 5","pages":"896-923"},"PeriodicalIF":1.2,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42273427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

Snaking without subcriticality: grain boundaries as non-topological defects 没有亚临界的蛇形:晶界作为非拓扑缺陷

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab032

Priya Subramanian;Andrew J Archer;Edgar Knobloch;Alastair M Rucklidge

{"title":"Snaking without subcriticality: grain boundaries as non-topological defects","authors":"Priya Subramanian;Andrew J Archer;Edgar Knobloch;Alastair M Rucklidge","doi":"10.1093/imamat/hxab032","DOIUrl":"10.1093/imamat/hxab032","url":null,"abstract":"Non-topological defects in spatial patterns such as grain boundaries in crystalline materials arise from local variations of the pattern properties such as amplitude, wavelength and orientation. Such non-topological defects may be treated as spatially localized structures, i.e. as fronts connecting distinct periodic states. Using the two-dimensional quadratic-cubic Swift–Hohenberg equation, we obtain fully nonlinear equilibria containing grain boundaries that separate a patch of hexagons with one orientation (the grain) from an identical hexagonal state with a different orientation (the background). These grain boundaries take the form of closed curves with multiple penta-hepta defects that arise from local orientation mismatches between the two competing hexagonal structures. Multiple isolas occurring robustly over a wide range of parameters are obtained even in the absence of a unique Maxwell point, underlining the importance of retaining pinning when analysing patterns with defects, an effect omitted from the commonly used amplitude-phase description. Similar results are obtained for quasiperiodic structures in a two-scale phase-field model.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 5","pages":"1164-1180"},"PeriodicalIF":1.2,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41636949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Spatial localization beyond steady states in the neighbourhood of the Takens–Bogdanov bifurcation Takens–Bogdanov分岔附近稳态以外的空间局部化

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab030

Haifaa Alrihieli;Alastair M Rucklidge;Priya Subramanian

{"title":"Spatial localization beyond steady states in the neighbourhood of the Takens–Bogdanov bifurcation","authors":"Haifaa Alrihieli;Alastair M Rucklidge;Priya Subramanian","doi":"10.1093/imamat/hxab030","DOIUrl":"10.1093/imamat/hxab030","url":null,"abstract":"Double-zero eigenvalues at a Takens–Bogdanov (TB) bifurcation occur in many physical systems such as double-diffusive convection, binary convection and magnetoconvection. Analysis of the associated normal form, in 1D with periodic boundary condition, shows the existence of steady patterns, standing waves, modulated waves (MW) and travelling waves, and describes the transitions and bifurcations between these states. Values of coefficients of the terms in the normal form classify all possible different bifurcation scenarios in the neighbourhood of the TB bifurcation (Dangelmayr, G. & Knobloch, E. (1987) The Takens–Bogdanov bifurcation with O(2)-symmetry. Phil. Trans. R. Soc. Lond. A, 322, 243-279). In this work we develop a new and simple pattern-forming partial differential equation (PDE) model, based on the Swift–Hohenberg equation, adapted to have the TB normal form at onset. This model allows us to explore the dynamics in a wide range of bifurcation scenarios, including in domains much wider than the lengthscale of the pattern. We identify two bifurcation scenarios in which coexistence between different types of solutions is indicated from the analysis of the normal form equation. In these scenarios, we look for spatially localized solutions by examining pattern formation in wide domains. We are able to recover two types of localized states, that of a localized steady state (LSS) in the background of the trivial state (TS) and that of a spatially localized travelling wave (LTW) in the background of the TS, which have previously been observed in other systems. Additionally, we identify two new types of spatially localized states: that of a LSS in a MW background and that of a LTW in a steady state (SS) background. The PDE model is easy to solve numerically in large domains and so will allow further investigation of pattern formation with a TB bifurcation in one or more dimensions and the exploration of a range of background and foreground pattern combinations beyond SSs.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 5","pages":"984-1009"},"PeriodicalIF":1.2,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48680311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Localized patterns in a generalized Swift–Hohenberg equation with a quartic marginal stability curve 具有四次边际稳定曲线的广义Swift–Hohenberg方程的局部化模式

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab035

David C Bentley;Alastair M Rucklidge

引用次数: 3

Localization and snaking in axially compressed and internally pressurized thin cylindrical shells 定位和蛇形在轴向压缩和内部加压薄圆柱壳

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-07-01 DOI: 10.1093/imamat/hxab024

Rainer M J Groh;Giles W Hunt

{"title":"Localization and snaking in axially compressed and internally pressurized thin cylindrical shells","authors":"Rainer M J Groh;Giles W Hunt","doi":"10.1093/imamat/hxab024","DOIUrl":"10.1093/imamat/hxab024","url":null,"abstract":"This paper uncovers new manifestations of the homoclinic snaking mechanism in the post-buckling regime of a pressurized thin cylindrical shell under axial load. These new forms tend to propagate either wholly or partially in a direction that is orthogonal to the direction of the applied load and so, unlike earlier forms in Woods & Champneys (1999, Heteroclinic tangles in the unfolding of a degenerate Hamiltonian Hopf bifurcation. Phys. D, 129, 147–170), are fundamentally 2D in nature. The main effect of internal pressurization on the snaking mechanism is firstly to transition the circumferential multiplication of buckles from a one-tier pattern to a three-tier pattern. Secondly, internal pressurization can induce oblique snaking, whereby the sequential multiplication of buckles occurs in a helical pattern across the cylinder domain. For low levels of internal pressure, the single dimple remains—as in the unpressurized case—the unstable edge state that forms the smallest energy barrier around the stable pre-buckling equilibrium. For greater levels of pressure, the edge state changes to a single dimple surrounded by four smaller dimples. By tracing the limit point that denotes the onset of these edge states in the parameter space of internal pressure and axial load, we justify and validate the empirically derived design guideline for buckling of pressurized cylinders proposed by Fung & Sechler (1957, Buckling of thin-walled circular cylinders under axial compression and internal pressure. J. Aeronaut. Sci., 24, 351–356).","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 5","pages":"1010-1030"},"PeriodicalIF":1.2,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47357326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1