Subjects -> MATHEMATICS (Total: 1105 journals)
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    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (814 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (25 journals)

MATHEMATICS (814 journals)            First | 1 2 3 4 5     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Computational Physics     Hybrid Journal   (Followers: 70)
Journal of Computational Physics : X     Open Access   (Followers: 1)
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 3)
Journal of Difference Equations and Applications     Hybrid Journal  
Journal of Differential Equations     Full-text available via subscription   (Followers: 1)
Journal of Discrete Algorithms     Hybrid Journal   (Followers: 4)
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 13)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 2)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 4)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 3)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 9)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 3)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 10)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 3)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 7)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access  
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 4)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
Journal of Progressive Research in Mathematics     Open Access   (Followers: 5)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 9)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 15)
Journal of Turbulence     Hybrid Journal   (Followers: 8)
Journal of Uncertainty Analysis and Applications     Open Access  
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 5)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 4)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access   (Followers: 3)
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 5)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 3)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal   (Followers: 1)
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematika     Open Access  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
Mathematical Journal of Interdisciplinary Sciences     Open Access  
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Models in Engineering     Open Access   (Followers: 5)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 3)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 2)
Mathematics Education Research Journal     Partially Free   (Followers: 18)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 7)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MathLAB Journal     Open Access   (Followers: 3)
MATI : Mathematical Aspects of Topological Indeces     Open Access  
MATICS     Open Access   (Followers: 2)
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal  
Metascience     Hybrid Journal   (Followers: 1)
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal   (Followers: 6)
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 1)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal   (Followers: 1)
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)
North Carolina Journal of Mathematics and Statistics     Open Access  

  First | 1 2 3 4 5     

Similar Journals
Journal Cover
Journal of Nonlinear Science
Journal Prestige (SJR): 1.568
Citation Impact (citeScore): 2
Number of Followers: 1  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-1467 - ISSN (Online) 0938-8974
Published by Springer-Verlag Homepage  [2626 journals]
  • Analysis of a Simplified Model of Rigid Structure Floating in a Viscous
    • Abstract: We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we propose a new model for this interaction, taking into consideration the viscosity of the fluid. This is done supposing that the flow obeys a shallow water regime (modeled by the viscous Saint-Venant equations in one space dimension) and using a Hamiltonian formalism. Another contribution of this work is establishing the well-posedness of the obtained PDEs/ODEs system in function spaces similar to the standard ones for strong solutions of viscous shallow water equations. Our well-posedness results are local in time for every initial data and global in time if the initial data are close (in appropriate norms) to an equilibrium state. Moreover, we show that the linearization of our system around an equilibrium state can be described, at least for some initial data, by an integro-fractional differential equation related to the classical Cummins equation and which reduces to the Cummins equation when the viscosity vanishes and the fluid is supposed to fill the whole space.
      PubDate: 2019-03-08
  • The Effects of Structural Perturbations on the Synchronizability of
           Diffusive Networks
    • Abstract: We investigate the effects of structural perturbations on the networks ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.
      PubDate: 2019-03-06
  • Localization in Adiabatic Shear Flow Via Geometric Theory of Singular
    • Abstract: We study localization occurring during high-speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition between Hadamard instability (caused by softening response) and the stabilizing effects of strain rate hardening. We consider a hyperbolic–parabolic system that expresses the above mechanism and construct self-similar solutions of localizing type that arise as the outcome of the above competition. The existence of self-similar solutions is turned, via a series of transformations, into a problem of constructing a heteroclinic orbit for an induced dynamical system. The dynamical system is in four dimensions but has a fast–slow structure with respect to a small parameter capturing the strength of strain rate hardening. Geometric singular perturbation theory is applied to construct the heteroclinic orbit as a transversal intersection of two invariant manifolds in the phase space.
      PubDate: 2019-03-04
  • Long-Time Asymptotics for Homoenergetic Solutions of the Boltzmann
           Equation: Collision-Dominated Case
    • Abstract: In this paper, we present a formal analysis of the long-time asymptotics of a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which have the form \(f\left( x,v,t\right) =g\left( v-L\left( t\right) x,t\right) \) where \(L\left( t\right) =A\left( I+tA\right) ^{-1}\) with the matrix A describing a shear flow or a dilatation or a combination of both. We began this study in James et al. (Arch Ration Mech Anal 231(2):787–843, 2019). Homoenergetic solutions satisfy an integro-differential equation which contains, in addition to the classical Boltzmann collision operator, a linear hyperbolic term. In James et al. (2019), it has been proved rigorously the existence of self-similar solutions which describe the change of the average energy of the particles of the system in the case in which there is a balance between the hyperbolic and the collision term. In this paper, we focus in homoenergetic solutions for which the collision term is much larger than the hyperbolic term (collision-dominated behavior). In this case, the long-time asymptotics for the distribution of velocities is given by a time-dependent Maxwellian distribution with changing temperature.
      PubDate: 2019-03-02
  • Calculating the Symmetry Number of Flexible Sphere Clusters
    • Abstract: We present a theoretical and computational framework to compute the symmetry number of a flexible sphere cluster in \({\mathbb {R}}^3\) , using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit. We define the sticky symmetry group of the cluster as the set of permutations and inversions of the spheres which preserve adjacency and can be realized by continuous deformations of the cluster that do not change the set of contacts or cause particles to overlap. The symmetry number is the size of the sticky symmetry group. We introduce a numerical algorithm to compute the sticky symmetry group and symmetry number, and show it works well on several test cases. Furthermore, we show that once the sticky symmetry group has been calculated for indistinguishable spheres, the symmetry group for partially distinguishable spheres (those with nonidentical interactions) can be efficiently obtained without repeating the laborious parts of the computations. We use our algorithm to calculate the partition functions of every possible connected cluster of six identical sticky spheres, generating data that may be used to design interactions between spheres so they self-assemble into a desired structure.
      PubDate: 2019-02-22
  • Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous
    • Abstract: We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness of the Doi model for large data and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity.
      PubDate: 2019-02-06
  • Nonlinear mechanics of accretion
    • Abstract: We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory, the material manifold of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material is added to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body. Balance laws are discussed and the initial boundary value problem of accretion is formulated. The particular cases where the growth surface is either fixed or traction-free are studied and some analytical results are provided. We numerically solve several accretion problems and calculate the residual stresses in nonlinear elastic bodies induced from accretion.
      PubDate: 2019-02-06
  • Editorial January 2019
    • PubDate: 2019-02-01
  • Variational Evolution of Dislocations in Single Crystals
    • Abstract: In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by means of integral one-currents. Moreover, we discuss a novel dissipation structure for such currents, namely the flat distance, that will serve to drive the evolution of the dislocation clusters.
      PubDate: 2019-02-01
  • Turbulent Cascade Direction and Lagrangian Time-Asymmetry
    • Abstract: We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time. These results are facilitated by a rigorous version of the Ott–Mann–Gawȩdzki relation, sometimes described as a “Lagrangian analogue of the 4 / 5-law.” In particular, we prove that for weak solutions of the Euler equations, the Lagrangian forward/backward dispersion measure matches onto the energy defect (Onsager in Nuovo Cimento (Supplemento) 6:279–287, 1949; Duchon and Robert in Nonlinearity 13(1):249–255, 2000) in the sense of distributions. For strong limits of \(d\ge 3\) -dimensional Navier–Stokes solutions, the defect distribution coincides with the viscous dissipation anomaly. The Lagrangian formula shows that particles released into a 3d turbulent flow will initially disperse faster backward in time than forward, in agreement with recent theoretical predictions of Jucha et al. (Phys Rev Lett 113(5):054501, 2014). In two dimensions, we consider strong limits of solutions of the forced Euler equations with increasingly high-wave number forcing as a model of an ideal inverse cascade regime. We show that the same Lagrangian dispersion measure matches onto the anomalous input from the infinite-frequency force. As forcing typically acts as an energy source, this leads to the prediction that particles in 2d typically disperse faster forward in time than backward, which is opposite to that which occurs in 3d. Time asymmetry of the Lagrangian dispersion is thereby closely tied to the direction of the turbulent cascade, downscale in \(d\ge 3\) and upscale in \(d=2\) . These conclusions lend support to the conjecture of Eyink and Drivas (J Stat Phys 158(2):386–432, 2015) that a similar connection holds for time asymmetry of Richardson two-particle dispersion and cascade direction.
      PubDate: 2019-02-01
  • Onsager’s Conjecture on the Energy Conservation for Solutions of Euler
           Equations in Bounded Domains
    • Abstract: The Onsager’s conjecture has two parts: conservation of energy, if the exponent is larger than 1 / 3, and the possibility of dissipative Euler solutions, if the exponent is less than or equal to 1 / 3. The paper proves half of the conjecture, the conservation part, in bounded domains.
      PubDate: 2019-02-01
  • Near-Integrability and Recurrence in FPU Chains with Alternating Masses
    • Abstract: An important aspect of understanding FPU chains is the existence of invariant manifolds (called “bushes”) in FPU chains. We will focus on the classical periodic FPU chain and on the FPU chain with alternating masses where we show that also in the alternating case nested manifolds (related to bushes) exist. The use of symmetries leads to the emergence of systems of n particles as invariant manifolds of systems with a multiple of n particles. This analysis is followed by examples of existence and stability of special invariant manifolds and phase-space dynamics in the case of 4 and 8 particles. These examples are typical for periodic FPU chains with 4n or 8n particles. It turns out that in the alternating case the dynamics is strongly affected by the choice of the alternating mass m. Normal form calculations help to identify quasi-trapping regions leading to delay of recurrence. The results suggest that equipartition of energy near stable equilibrium is improbable.
      PubDate: 2019-02-01
  • Stochastic Evolution of Augmented Born–Infeld Equations
    • Abstract: This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born–Infeld model of nonlinear electromagnetism. The similarities in the results are striking. Namely, the introduction of Stratonovich cylindrical noise into each of their Hamiltonian formulations introduces stochastic Lie transport into their dynamics in the same form for both theories. Moreover, the resulting stochastic partial differential equations retain their unperturbed form, except for an additional term representing induced Lie transport by the set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation for this remarkable similarity lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, which is done via pairing spatial correlation eigenvectors for cylindrical noise with the momentum map for the deterministic motion. This momentum map is responsible for the well-known analogy between hydrodynamics and electromagnetism. The momentum map for the Maxwell and Born–Infeld theories of electromagnetism treated here is the 1-form density known as the Poynting vector. Two appendices treat the Hamiltonian structures underlying these results.
      PubDate: 2019-02-01
  • Advection and Autocatalysis as Organizing Principles for Banded Vegetation
    • Abstract: We motivate and analyze a simple model for the formation of banded vegetation patterns. The model incorporates a minimal number of ingredients for vegetation growth in semiarid landscapes. It allows for comprehensive analysis and sheds new light onto phenomena such as the migration of vegetation bands and the interplay between their upper and lower edges. The key ingredient is the formulation as a closed reaction–diffusion system, thus introducing a conservation law that both allows for analysis and provides ready intuition and understanding through analogies with characteristic speeds of propagation and shock waves.
      PubDate: 2019-02-01
  • Reduced One-Dimensional Models for Wave Turbulence System
    • Abstract: While studying many wave turbulence (WT) phenomena, owing to their inherent complexity, one frequently encounters the necessity of uncertainty quantification (UQ) in high dimension. The implementation of many existing algorithms for the UQ under these circumstances demands a vast amount of computation and, as a consequence, the straightforward approach tends to be infeasible or impractical. One effort to circumvent this obstacle in high dimension is to find an effective dimension reduction procedure for the probability distribution of the dynamical system model. One of the methodologies to do this is to replace the true Markovian model with a simple stochastic model that is significantly more amenable to the UQ than the underlying system. The procedure can be carried out via approximating the original equation for each Fourier mode by an independent and analytically tractable stochastic differential equation. In this work, we introduce a new approach for the so-called reduced-order model strategy within the context of the Majda–McLaughlin–Tabak model. Our framework makes use of a detailed analysis of the one-dimensional WT prototype to build a family of simplified models. Furthermore, the adaptive parameters are tuned without performing a direct numerical simulation of the true dynamical system model.
      PubDate: 2019-02-01
  • Backward Parabolicity, Cross-Diffusion and Turing Instability
    • Abstract: We show that the ill-posedness observed in backward parabolic equation, or cross-diffusion systems, can be interpreted as a limiting Turing instability for a corresponding semi-linear parabolic system. Our analysis is based on the, now well established, derivation of nonlinear parabolic and cross-diffusion systems from semi-linear reaction–diffusion systems with fast reaction rates. We illustrate our observation with two generic examples for \(2\times 2\) and \(4\times 4\) reaction–diffusion systems. For these examples, we prove that backward parabolicity in cross-diffusion systems is equivalent to Turing instability for fast reaction rates. In one dimension, the Turing patterns are periodic solutions which have frequencies which increase with the reaction rate. Furthermore, in some specific cases, the structure of the equations at hand involves classical entropy/Lyapunov functions which lead to a priori estimates allowing to pass rigorously to the fast reaction limit in the absence of Turing instabilities.
      PubDate: 2019-02-01
  • Weak and Strong Solutions of the 3 D Navier–Stokes Equations and Their
           Relation to a Chessboard of Convergent Inverse Length Scales
    • Abstract: Using the scale invariance of the Navier–Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the 3D Navier–Stokes equations, on a periodic domain \(\mathcal {V} =[0,\,L]^{3}\) an infinite ‘chessboard’ of estimates for these inverse length scales is displayed in terms of labels \((n,\,m)\) corresponding to n derivatives of the velocity field in \(L^{2m}(\mathcal {V})\) . The \((1,\,1)\) position corresponds to the inverse Kolmogorov length \(Re^{3/4}\) . These estimates ultimately converge to a finite limit, \(Re^3\) , as \(n,\,m\rightarrow \infty \) , although this limit is too large to lie within the physical validity of the equations for realistically large Reynolds numbers. Moreover, all the known time-averaged estimates for weak solutions can be rolled into one single estimate, labelled by \((n,\,m)\) . In contrast, those required for strong solutions to exist can be written in another single estimate, also labelled by \((n,\,m)\) , the only difference being a factor of 2 in the exponent. This appears to be a generalization of the Prodi–Serrin conditions for \(n\ge 1\) .
      PubDate: 2019-02-01
  • Bifurcations in a Diffusive Predator–Prey Model with
           Beddington–DeAngelis Functional Response and Nonselective Harvesting
    • Abstract: In this paper, we discuss the dynamics of a predator–prey model with Beddington–DeAngelis functional response and nonselective harvesting. By using the Lyapunov–Schmidt reduction, we obtain the existence of spatially nonhomogeneous steady-state solution. The stability and existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the change of a specific parameter are investigated by analyzing the distribution of the eigenvalues. We also get an algorithm for determining the bifurcation direction of the Hopf bifurcating periodic solutions near the nonhomogeneous steady-state solution. Finally, we show some numerical simulations to verify our analytical results.
      PubDate: 2019-02-01
  • A Reaction–Diffusion Model of Vector-Borne Disease with Periodic
    • Abstract: A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion model of vector-borne disease with periodic delays. We introduce the basic reproduction number \(\mathfrak {R}_0\) for this model and then establish a threshold-type result on its global dynamics in terms of \(\mathfrak {R}_0\) . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when \(\mathfrak {R}_0>1\) . Numerically, we study the malaria transmission in Maputo Province, Mozambique.
      PubDate: 2019-02-01
  • The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy
    • Authors: Chunxia Li; Shi-Hao Li
      Abstract: This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the \(\tau \) -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.
      PubDate: 2018-06-01
      DOI: 10.1007/s00332-018-9474-x
School of Mathematical and Computer Sciences
Heriot-Watt University
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