Subjects -> PHYSICS (Total: 898 journals)
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PHYSICS (659 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 741 Journals sorted alphabetically
Acta Acustica united with Acustica     Full-text available via subscription   (Followers: 7)
Acta Mechanica     Hybrid Journal   (Followers: 25)
Acta Scientifica Naturalis     Open Access   (Followers: 3)
Advanced Composite Materials     Hybrid Journal   (Followers: 76)
Advanced Electronic Materials     Hybrid Journal   (Followers: 2)
Advanced Functional Materials     Hybrid Journal   (Followers: 68)
Advanced Materials     Hybrid Journal   (Followers: 374)
Advanced Nonlinear Studies     Hybrid Journal  
Advanced Quantum Technologies     Hybrid Journal  
Advanced Science Focus     Free   (Followers: 6)
Advanced Structural and Chemical Imaging     Open Access   (Followers: 2)
Advanced Studies in Theoretical Physics     Open Access   (Followers: 3)
Advanced Theory and Simulations     Hybrid Journal   (Followers: 1)
Advances in Clinical Radiology     Full-text available via subscription   (Followers: 2)
Advances in Condensed Matter Physics     Open Access   (Followers: 11)
Advances in Exploration Geophysics     Full-text available via subscription   (Followers: 2)
Advances in Geophysics     Full-text available via subscription   (Followers: 8)
Advances in High Energy Physics     Open Access   (Followers: 22)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 4)
Advances in Materials Physics and Chemistry     Open Access   (Followers: 31)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 30)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in OptoElectronics     Open Access   (Followers: 6)
Advances In Physics     Hybrid Journal   (Followers: 25)
Advances in Physics : X     Open Access   (Followers: 5)
Advances in Physics Theories and Applications     Open Access   (Followers: 19)
Advances in Remote Sensing     Open Access   (Followers: 55)
AIP Advances     Open Access   (Followers: 10)
AIP Conference Proceedings     Full-text available via subscription   (Followers: 4)
American Journal of Condensed Matter Physics     Open Access   (Followers: 7)
American Journal of Signal Processing     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Anales (Asociación Física Argentina)     Open Access  
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Annalen der Physik     Hybrid Journal   (Followers: 6)
Annales Geophysicae (ANGEO)     Open Access   (Followers: 19)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 4)
Annals of Physics     Hybrid Journal   (Followers: 6)
Annals of West University of Timisoara - Physics     Open Access   (Followers: 1)
Annual Reports on NMR Spectroscopy     Full-text available via subscription   (Followers: 5)
Annual Review of Analytical Chemistry     Full-text available via subscription   (Followers: 12)
Annual Review of Condensed Matter Physics     Full-text available via subscription   (Followers: 4)
Annual Review of Materials Research     Full-text available via subscription   (Followers: 7)
APL Materials     Open Access   (Followers: 15)
Applied Composite Materials     Hybrid Journal   (Followers: 53)
Applied Physics     Open Access   (Followers: 6)
Applied Physics A     Hybrid Journal   (Followers: 10)
Applied Physics Frontier     Open Access   (Followers: 4)
Applied Physics Letters     Hybrid Journal   (Followers: 43)
Applied Physics Research     Open Access   (Followers: 6)
Applied Physics Reviews     Hybrid Journal   (Followers: 8)
Applied Radiation and Isotopes     Hybrid Journal   (Followers: 7)
Applied Spectroscopy     Full-text available via subscription   (Followers: 26)
Applied Spectroscopy Reviews     Hybrid Journal   (Followers: 4)
Archive for Rational Mechanics and Analysis     Hybrid Journal  
Asia Pacific Physics Newsletter     Hybrid Journal   (Followers: 1)
Asian Journal of Physical and Chemical Sciences     Open Access   (Followers: 1)
ASTRA Proceedings     Open Access   (Followers: 2)
Astronomy & Geophysics     Hybrid Journal   (Followers: 47)
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 23)
Astrophysical Journal Letters     Full-text available via subscription   (Followers: 12)
Astrophysical Journal Supplement Series     Full-text available via subscription   (Followers: 12)
Atoms     Open Access   (Followers: 1)
Attention, Perception & Psychophysics     Full-text available via subscription   (Followers: 15)
Axioms     Open Access   (Followers: 1)
Bangladesh Journal of Medical Physics     Open Access   (Followers: 1)
Bauphysik     Hybrid Journal   (Followers: 1)
Berkala Fisika Indonesia     Open Access  
Biomaterials     Hybrid Journal   (Followers: 50)
Biomedical Imaging and Intervention Journal     Open Access   (Followers: 4)
Biophysical Reviews     Hybrid Journal   (Followers: 1)
Biophysical Reviews and Letters     Hybrid Journal   (Followers: 3)
BJR|Open     Open Access   (Followers: 1)
BMC Biophysics     Open Access   (Followers: 3)
Boson Journal of Modern Physics     Open Access   (Followers: 10)
Brazilian Journal of Physics     Hybrid Journal   (Followers: 1)
Buletin Fisika     Open Access  
Bulletin of Materials Science     Open Access   (Followers: 43)
Bulletin of the Atomic Scientists     Hybrid Journal   (Followers: 5)
Bulletin of the Lebedev Physics Institute     Hybrid Journal   (Followers: 2)
Bulletin of the Russian Academy of Sciences: Physics     Hybrid Journal   (Followers: 3)
Caderno Brasileiro de Ensino de Física     Open Access  
Canadian Journal of Physics     Hybrid Journal   (Followers: 14)
Case Studies in Nondestructive Testing and Evaluation     Open Access   (Followers: 11)
Cells     Open Access   (Followers: 3)
CERN courier. International journal of high energy physics     Free   (Followers: 8)
Chemical Physics Letters : X     Open Access   (Followers: 2)
Chemical Physics of Solid Surfaces     Full-text available via subscription  
Chinese Journal of Astronomy and Astrophysics     Full-text available via subscription   (Followers: 15)
Chinese Journal of Chemical Physics     Hybrid Journal   (Followers: 1)
Chinese Journal of Physics     Hybrid Journal   (Followers: 1)
Chinese Physics B     Full-text available via subscription   (Followers: 1)
Chinese Physics C     Full-text available via subscription   (Followers: 1)
Chinese Physics Letters     Full-text available via subscription   (Followers: 1)
Ciencia     Open Access   (Followers: 1)
Cogent Physics     Open Access   (Followers: 2)
Cohesion and Structure     Full-text available via subscription   (Followers: 2)
Colloid Journal     Hybrid Journal   (Followers: 3)
Communications in Computational Physics     Full-text available via subscription   (Followers: 3)
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications in Numerical Methods in Engineering     Hybrid Journal   (Followers: 2)
Communications in Theoretical Physics     Full-text available via subscription   (Followers: 5)
Communications Materials     Open Access   (Followers: 2)
Communications Physics     Open Access  
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 259)
Composites Part B : Engineering     Hybrid Journal   (Followers: 300)
Computational Astrophysics and Cosmology     Open Access   (Followers: 2)
Computational Condensed Matter     Open Access  
Computational Materials Science     Hybrid Journal   (Followers: 23)
Computational Mathematics and Mathematical Physics     Hybrid Journal   (Followers: 4)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computer Physics Communications     Hybrid Journal   (Followers: 8)
Condensed Matter     Open Access   (Followers: 2)
Contemporary Concepts of Condensed Matter Science     Full-text available via subscription  
Contemporary Physics     Hybrid Journal   (Followers: 26)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 8)
Contributions to Plasma Physics     Hybrid Journal   (Followers: 6)
COSPAR Colloquia Series     Full-text available via subscription   (Followers: 10)
Cryogenics     Hybrid Journal   (Followers: 58)
Current Applied Physics     Full-text available via subscription   (Followers: 5)
Current Science     Open Access   (Followers: 105)
Diagnostic and Interventional Imaging     Full-text available via subscription  
Diamond and Related Materials     Hybrid Journal   (Followers: 12)
Discrete and Continuous Models and Applied Computational Science     Open Access   (Followers: 1)
Doklady Physics     Hybrid Journal   (Followers: 2)
Dynamical Properties of Solids     Full-text available via subscription  
e-Boletim da Física     Open Access   (Followers: 1)
East European Journal of Physics     Open Access  
ECS Journal of Solid State Science and Technology     Hybrid Journal   (Followers: 8)
Edufisika : Jurnal Pendidikan Fisika     Open Access   (Followers: 1)
Egyptian Journal of Remote Sensing and Space Science     Open Access   (Followers: 22)
EJNMMI Physics     Open Access   (Followers: 1)
Electrospinning     Open Access  
Emergent Scientist     Open Access   (Followers: 1)
Energy Procedia     Open Access   (Followers: 4)
Engineering Failure Analysis     Hybrid Journal   (Followers: 67)
Engineering Fracture Mechanics     Hybrid Journal   (Followers: 26)
Environmental Fluid Mechanics     Hybrid Journal   (Followers: 6)
Environmental Research Communications     Open Access  
EPJ Nonlinear Biomedical Physics     Open Access  
EPJ Quantum Technology     Open Access   (Followers: 1)
EPJ Techniques and Instrumentation     Open Access  
EPJ Web of Conferences     Open Access   (Followers: 1)
EUREKA : Physics and Engineering     Open Access   (Followers: 1)
European Journal of Physics     Full-text available via subscription   (Followers: 20)
European Physical Journal - Applied Physics     Full-text available via subscription   (Followers: 18)
European Physical Journal C     Hybrid Journal   (Followers: 1)
Europhysics News     Open Access  
Experimental and Computational Multiphase Flow     Hybrid Journal  
Experimental Mechanics     Hybrid Journal   (Followers: 23)
Experimental Methods in the Physical Sciences     Full-text available via subscription  
Experimental Techniques     Hybrid Journal   (Followers: 54)
Exploration Geophysics     Hybrid Journal   (Followers: 5)
Few-Body Systems     Hybrid Journal   (Followers: 1)
Fire and Materials     Hybrid Journal   (Followers: 5)
Flexible Services and Manufacturing Journal     Hybrid Journal   (Followers: 1)
Fluctuation and Noise Letters     Hybrid Journal   (Followers: 1)
Fluid Dynamics     Hybrid Journal   (Followers: 23)
Fortschritte der Physik/Progress of Physics     Hybrid Journal  
Frontiers in Nanotechnology     Open Access   (Followers: 1)
Frontiers in Physics     Open Access   (Followers: 6)
Frontiers of Materials Science     Hybrid Journal   (Followers: 4)
Frontiers of Physics     Hybrid Journal   (Followers: 2)
Fusion Engineering and Design     Hybrid Journal   (Followers: 10)
Geochemistry, Geophysics, Geosystems     Full-text available via subscription   (Followers: 32)
Geografiska Annaler, Series A : Physical Geography     Hybrid Journal   (Followers: 3)
Geophysical Research Letters     Full-text available via subscription   (Followers: 184)
Glass Physics and Chemistry     Hybrid Journal   (Followers: 4)
Granular Matter     Hybrid Journal   (Followers: 1)
Graphs and Combinatorics     Hybrid Journal   (Followers: 6)
Gravitation and Cosmology     Hybrid Journal   (Followers: 4)
Handbook of Geophysical Exploration: Seismic Exploration     Full-text available via subscription  
Handbook of Metal Physics     Full-text available via subscription  
Handbook of Surface Science     Full-text available via subscription   (Followers: 4)
Handbook of Thermal Analysis and Calorimetry     Full-text available via subscription   (Followers: 1)
Heat Transfer - Asian Research     Hybrid Journal   (Followers: 11)
High Energy Density Physics     Hybrid Journal   (Followers: 2)
High Pressure Research: An International Journal     Hybrid Journal   (Followers: 3)
IEEE Embedded Systems Letters     Hybrid Journal   (Followers: 56)
IEEE Journal of Quantum Electronics     Hybrid Journal   (Followers: 22)
IEEE Journal on Multiscale and Multiphysics Computational Techniques     Hybrid Journal   (Followers: 2)
IEEE Magnetics Letters     Hybrid Journal   (Followers: 7)
IEEE Nanotechnology Magazine     Hybrid Journal   (Followers: 42)
IEEE Reviews in Biomedical Engineering     Hybrid Journal   (Followers: 22)
IEEE Signal Processing Magazine     Full-text available via subscription   (Followers: 87)
IEEE Solid-State Circuits Magazine     Hybrid Journal   (Followers: 13)
IEEE Transactions on Autonomous Mental Development     Hybrid Journal   (Followers: 8)
IEEE Transactions on Biomedical Engineering     Hybrid Journal   (Followers: 38)
IEEE Transactions on Broadcasting     Hybrid Journal   (Followers: 13)
IEEE Transactions on Geoscience and Remote Sensing     Hybrid Journal   (Followers: 221)
IEEE Transactions on Haptics     Hybrid Journal   (Followers: 4)
IEEE Transactions on Industrial Electronics     Hybrid Journal   (Followers: 76)
IEEE Transactions on Industry Applications     Hybrid Journal   (Followers: 40)
IEEE Transactions on Learning Technologies     Full-text available via subscription   (Followers: 12)
IEEE Transactions on Quantum Engineering     Open Access   (Followers: 2)
IEEE Transactions on Services Computing     Hybrid Journal   (Followers: 4)
IEEE Transactions on Software Engineering     Hybrid Journal   (Followers: 79)

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Similar Journals
Journal Cover
Archive for Rational Mechanics and Analysis
Journal Prestige (SJR): 3.93
Citation Impact (citeScore): 3
Number of Followers: 0  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0673 - ISSN (Online) 0003-9527
Published by Springer-Verlag Homepage  [2624 journals]
  • Quasilinear SPDEs via Rough Paths
    • Abstract: Abstract We are interested in (uniformly) parabolic PDEs with a nonlinear dependence of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a space-time periodic setting with a single spatial variable: $$\partial_2u -P( a(u)\partial_1^2u + \sigma(u)f ) =0,$$ where P is the projection on mean-zero functions, and f is a distribution which is only controlled in the low regularity norm of \({ C^{\alpha-2}}\) for \({\alpha > \frac{2}{3}}\) on the parabolic Hölder scale. The example we have in mind is a random forcing f and our assumptions allow, for example, for an f which is white in the time variable x2 and only mildly coloured in the space variable x1; any spatial covariance operator \({(1 + \partial_1 )^{-\lambda_1 }}\) with \({\lambda_1 > \frac13}\) is admissible. On the deterministic side we obtain a \({C^\alpha}\) -estimate for u, assuming that we control products of the form \({v\partial_1^2v}\) and vf with v solving the constant-coefficient equation \({\partial_2 v-a_0\partial_1^2v=f}\) . As a consequence, we obtain existence, uniqueness and stability with respect to \({(f, vf, v \partial_1^2v)}\) of small space-time periodic solutions for small data. We then demonstrate how the required products can be bounded in the case of a random forcing f using stochastic arguments. For this we extend the treatment of the singular product \({\sigma(u)f}\) via a space-time version of Gubinelli’s notion of controlled rough paths to the product \({a(u)\partial_1^2u}\) , which has the same degree of singularity but is more nonlinear since the solution u appears in both factors. In fact, we develop a theory for the linear equation \({\partial_t u - P(a\partial_1^2 u +\sigma f)=0}\) with rough but given coefficient fields a and \({\sigma}\) and then apply a fixed point argument. The PDE ingredient mimics the (kernel-free) Safonov approach to ordinary Schauder theory.
      PubDate: 2019-05-01
  • A Priori Estimates for Water Waves with Emerging Bottom
    • Abstract: Abstract We study the beach problem for water waves. The case we consider is a compact fluid domain, where the free surface intersects the bottom along an edge, with a non-zero contact angle. Using elliptic estimates in domains with edges and a new equation on the Taylor coefficient, we establish a priori estimates for angles smaller than a dimensional constant. Local existence will be derived in a following paper.
      PubDate: 2019-05-01
  • Incompressible Jet Flows in a de Laval Nozzle with Smooth Detachment
    • Abstract: Abstract In this paper, we are concerned with the well-posedness theory of steady incompressible jet flow in a de Laval type nozzle with given end pressure at the outlet. The main results show that for any given incoming mass flux Q > 0 in the upstream and end pressure at the outlet, there exists an admissible interval to the Bernoulli’s constant, if the Bernoulli’s constant lies in the interval, there exists a unique smooth incompressible jet flow issuing from the nozzle. Moreover, the free boundary of the jet flow initiates smoothly from the surface of the divergent area of the de Laval nozzle. In particular, it is shown that the initial point of the free boundary lies behind the throat of the de Laval nozzle wall and varies continuously and monotonically with respect to the Bernoulli’s constant. As a direct corollary, imposing initial point of the free boundary on the divergent part of nozzle wall, there exists a unique incompressible jet for given incoming mass flux Q > 0 and pressure Pe at the outlet. This work is inspired by the significant works (Alt et al. in Commun Pure Appl Math 35:29–68, 1982; Arch Rational Mech Anal 81:97–149, 1983) for the incompressible jet flow imposing the initial point of the free boundary at the endpoint of the nozzle.
      PubDate: 2019-05-01
  • Non-existence of Classical Solutions with Finite Energy to the Cauchy
           Problem of the Compressible Navier–Stokes Equations
    • Abstract: Abstract The well-posedness of classical solutions with finite energy to the compressible Navier–Stokes equations (CNS) subject to arbitrarily large and smooth initial data is a challenging problem. In the case when the fluid density is away from vacuum (strictly positive), this problem was first solved for the CNS in either one-dimension for general smooth initial data or multi-dimension for smooth initial data near some equilibrium state (that is, small perturbation) (Antontsev et al. in Boundary value problems in mechanics of nonhomogeneous fluids, North-Holland Publishing Co., Amsterdam, 1990; Kazhikhov in Sibirsk Mat Zh 23:60–64, 1982; Kazhikhov et al. in Prikl Mat Meh 41:282–291, 1977; Matsumura and Nishida in Proc Jpn Acad Ser A Math Sci 55:337–342, 1979, J Math Kyoto Univ 20:67–104, 1980, Commun Math Phys 89:445–464, 1983). In the case that the flow density may contain a vacuum (the density can be zero at some space-time point), it seems to be a rather subtle problem to deal with the well-posedness problem for CNS. The local well-posedness of classical solutions containing a vacuum was shown in homogeneous Sobolev space (without the information of velocity in L2-norm) for general regular initial data with some compatibility conditions being satisfied initially (Cho et al. in J Math Pures Appl (9) 83:243–275, 2004; Cho and Kim in J Differ Equ 228:377–411, 2006, Manuscr Math 120:91–129, 2006; Choe and Kim in J Differ Equ 190:504–523 2003), and the global existence of a classical solution in the same space is established under the additional assumption of small total initial energy but possible large oscillations (Huang et al. in Commun Pure Appl Math 65:549–585, 2012). However, it was shown that any classical solutions to the compressible Navier–Stokes equations in finite energy (inhomogeneous Sobolev) space cannot exist globally in time since it may blow up in finite time provided that the density is compactly supported (Xin in Commun Pure Appl Math 51:229–240, 1998). In this paper, we investigate the well-posedess of classical solutions to the Cauchy problem of Navier–Stokes equations, and prove that the classical solution with finite energy does not exist in the inhomogeneous Sobolev space for any short time under some natural assumptions on initial data near the vacuum. This implies, in particular, that the homogeneous Sobolev space is as crucial as studying the well-posedness for the Cauchy problem of compressible Navier–Stokes equations in the presence of a vacuum at far fields even locally in time.
      PubDate: 2019-05-01
  • Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional
           Minkowski Spacetime
    • Abstract: Abstract We are concerned with the nonlinear stability of vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. This is a nonlinear hyperbolic problem with a characteristic free boundary. In this paper, we introduce a new symmetrization by choosing appropriate functions as primary unknowns. A necessary and sufficient condition for the weakly linear stability of relativistic vortex sheets is obtained by analyzing the roots of the Lopatinskiĭ determinant associated to the constant coefficient linearized problem. Under this stability condition, we show that the variable coefficient linearized problem obeys an energy estimate with a loss of derivatives. The construction of certain weight functions plays a crucial role in absorbing the error terms caused by microlocalization. Based on the weakly linear stability result, we establish the existence and nonlinear stability of relativistic vortex sheets under small initial perturbations by a Nash–Moser iteration scheme.
      PubDate: 2019-05-01
  • Analysis of Diffusion Generated Motion for Mean Curvature Flow in
           Codimension Two: A Gradient-Flow Approach
    • Abstract: Abstract The Merriman–Bence–Osher (MBO) scheme, also known as diffusion generated motion or thresholding, is an efficient numerical algorithm for computing mean curvature flow (MCF). It is fairly well understood in the case of hypersurfaces. This paper establishes the first convergence proof of the scheme in codimension two. We concentrate on the case of the curvature motion of a filament (curve) in \({{\mathbb{R}}^3}\) . Our proof is based on a new generalization of the minimizing movements interpretation for hypersurfaces (Esedoglu–Otto ’15) by means of an energy that approximates the Dirichlet energy of the state function. As long as a smooth MCF exists, we establish uniform energy estimates for the approximations away from the smooth solution and prove convergence towards this MCF. The current result that holds in codimension two relies in a very crucial manner on a new sharp monotonicity formula for the thresholding energy. This is an improvement of an earlier approximate version.
      PubDate: 2019-05-01
  • Suppressing Chemotactic Blow-Up Through a Fast Splitting Scenario on the
    • Abstract: Abstract We revisit the question of global regularity for the Patlak–Keller–Segel (PKS) chemotaxis model. The classical 2D parabolic-elliptic model blows up for initial mass \({M > 8\pi}\) . We consider a more realistic scenario which takes into account the flow of the ambient environment induced by harmonic potentials, and thus retain the identical elliptic structure as in the original PKS. Surprisingly, we find that already the simplest case of linear stationary vector field, \({Ax^\top}\) , with large enough amplitude \({A}\) , prevents chemotactic blow-up. Specifically, the presence of such an ambient fluid transport creates what we call a ‘fast splitting scenario’, which competes with the focusing effect of aggregation so that ‘enough mass’ is pushed away from concentration along the \({x_1}\) -axis, thus avoiding a finite time blow-up, at least for \({M < 16\pi}\) . Thus, the enhanced ambient flow doubles the amount of allowable mass which evolve to global smooth solutions.
      PubDate: 2019-05-01
  • Global Structure and Regularity of Solutions to the Eikonal Equation
    • Abstract: Abstract The evolutionary Eikonal equation is a Hamilton–Jacobi equation with Hamiltonian H(P) =  P , which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly convex Hamiltonians, therefore leading to new phenomena. In this paper, we study the set of singularity points of solutions in the upper half space for C1 or C2 initial data, with emphasis on the countability of connected components of the set. The regularity of solutions in the complement of the set of singularity points is also obtained.
      PubDate: 2019-05-01
  • On the Regularity of the Minimizer of the Electrostatic Born–Infeld
    • Abstract: Abstract We consider the electrostatic Born–Infeld energy $$\int_{\mathbb{R}^N}\left(1-{\sqrt{1- \nabla u ^2}}\right)\, {\rm d}x -\int_{\mathbb{R}^N}\rho u\, {\rm d}x,$$ where \({\rho \in L^{m}(\mathbb{R}^N)}\) is an assigned charge density, \({m \in [1,2_*]}\) , \({2_*:=\frac{2N}{N+2}}\) , \({N\geq 3}\) . We prove that if \({\rho \in L^q(\mathbb{R}^N) }\) for \({q > 2N}\) , the unique minimizer \({u_\rho}\) is of class \({W_{loc}^{2,2}(\mathbb{R}^N)}\) . Moreover, if the norm of \({\rho}\) is sufficiently small, the minimizer is a weak solution of the associated PDE $$\label{eq:BI-abs}-\operatorname{div}\left(\displaystyle\frac{\nabla u}{\sqrt{1- \nabla u ^2}}\right)= \rho \quad\hbox{in }\mathbb{R}^N,\quad \quad \quad \mathcal{(BI)}$$ with the boundary condition \({\lim_{ x \to\infty}u(x)=0}\) , and it is of class \({C^{1,\alpha}_{loc}(\mathbb{R}^N)}\) for some \({\alpha \in (0,1)}\) .
      PubDate: 2019-05-01
  • Stochastic Homogenization for Reaction–Diffusion Equations
    • Abstract: Abstract In the present paper we study stochastic homogenization for reaction–diffusion equations with stationary ergodic reactions (including periodic). We first show that under suitable hypotheses, initially localized solutions to the PDE asymptotically become approximate characteristic functions of a ballistically expanding Wulff shape. The next crucial component is the proper definition of relevant front speeds and the subsequent establishment of their existence. We achieve the latter by finding a new relation between the front speeds and the Wulff shape, provided the Wulff shape does not have corners. Once front speeds are proved to exist in all directions, by the above means or otherwise, we are able to obtain general stochastic homogenization results, showing that large space–time evolution of solutions to the PDE is governed by a simple deterministic Hamilton–Jacobi equation whose Hamiltonian is given by these front speeds. Our results are new even for periodic reactions, particularly of ignition type. We primarily consider the case of non-negative reactions but we also extend our results to the more general PDE \({u_{t}= F(D^2 u,\nabla u,u,x,\omega)}\) , as long as its solutions satisfy some basic hypotheses including positive lower and upper bounds on spreading speeds in all directions and a sub-ballistic bound on the width of the transition zone between the two equilibria of the PDE.
      PubDate: 2019-05-01
  • Finite-Energy Solutions for Compressible Two-Fluid Stokes System
    • Abstract: Abstract We prove the existence of global in time weak solutions to a compressible two-fluid Stokes system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. The system appears to be outside the class of problems that can be treated using the classical Lions–Feireisl approach. Adapting the novel compactness tool developed by the first author and P.-E. Jabin in the mono-fluid compressible Navier–Stokes setting, we first prove the weak sequential stability of solutions. Next, we construct weak solutions via an unconventional approximation using the Lagrangian formulation, truncations, and a stability result of trajectories for rough velocity fields.
      PubDate: 2019-05-01
  • Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular
    • Abstract: Abstract We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling for which the transition from single domain to multidomain ground states such as bubble or maze patterns occurs as the film thickness goes to zero and the lateral extent goes to infinity. Furthermore, we analyze the asymptotic behavior of the energy in these two asymptotic regimes. In the single domain regime, the energy Γ-converges towards a much simpler two-dimensional and local model. In the multidomain regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.
      PubDate: 2019-05-01
  • Twisted Solutions to a Simplified Ericksen–Leslie Equation
    • Abstract: Abstract In this article we construct global solutions to a simplified Ericksen–Leslie system on \({\mathbb{R}^3}\) . The constructed solutions are twisted and periodic along the x3-axis with period \({d = 2\pi \big/ \mu}\) . Here \({\mu > 0}\) is the twist rate and d is the distance between two planes which are parallel to the x1x2-plane. Liquid crystal material is placed in the region enclosed by these two planes. Given a well-prepared initial data, our solutions exist classically for all \({t \in (0, \infty)}\) . However, these solutions become singular at all points on the x3-axis and escape into third dimension exponentially while \({t \rightarrow \infty}\) . An optimal blow up rate is also obtained.
      PubDate: 2019-04-01
  • A Free Boundary Problem with Facets
    • Abstract: Abstract We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove that the solutions are unique, and prove that the limiting free boundary has a facets in every rational direction. Our choice of problem presents difficulties that require the development of a new uniqueness proof for certain free boundary problems. The problem is motivated by physical experiments involving liquid drops on patterned solid surfaces.
      PubDate: 2019-04-01
  • Global Weak Besov Solutions of the Navier–Stokes Equations and
    • Abstract: Abstract We introduce a notion of global weak solution to the Navier–Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces \({\dot{B}^{-1+\frac{3}{p}}_{p,\infty}}\) , p >  3. These solutions satisfy a certain stability property with respect to the weak- \({\ast}\) convergence of initial conditions. To illustrate this property, we provide applications to blow-up criteria, minimal blow-up initial data, and forward self-similar solutions. Our proof relies on a new splitting result in homogeneous Besov spaces that may be of independent interest.
      PubDate: 2019-04-01
  • Two-Phase Solutions for One-Dimensional Non-convex Elastodynamics
    • Abstract: Abstract We explore the local existence and properties of classical weak solutions to the initial-boundary value problem for a class of quasilinear equations of elastodynamics in one space dimension with a non-convex stored-energy function, a model of phase transitions in elastic bars proposed by Ericksen (J Elast 5(3–4):191–201,1975). The instantaneous phase separation and formation of microstructures of such solutions are observed for all smooth initial data with initial strain having its range that overlaps with the phase transition zone of the Piola–Kirchhoff stress. Moreover, we can select those solutions in a way that their phase gauges are close to a certain number inherited from a modified hyperbolic problem and thus give rise to an internal strain–stress hysteresis loop. As a byproduct, we prove the existence of a measure-valued solution to the problem that is generated by a sequence of weak solutions but not a weak solution itself. It is also shown that the problem admits a local weak solution for all smooth initial data and local weak solutions that are smooth for a short period of time and exhibit microstructures thereafter for certain smooth initial data.
      PubDate: 2019-04-01
  • The Effect of Forest Dislocations on the Evolution of a Phase-Field Model
           for Plastic Slip
    • Abstract: Abstract We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls–Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The \({\Gamma}\) -limit of this energy was deduced by Garroni and Müller (SIAM J Math Anal 36(6):1943–1964, 2005, Arch Ration Mech Anal 181(3):535–578, 2006). Our main result shows that the gradient flows of these \({\Gamma}\) -convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-monotone loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen–Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the \({\Gamma}\) -limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.
      PubDate: 2019-04-01
  • Global Existence of Quasi-Stratified Solutions for the Confined IPM
    • Abstract: Abstract In this paper, we consider a confined physical scenario to prove the global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the stability of stratified solutions, combined with an additional structure of our initial perturbation, which allows us to get rid of the boundary terms in the energy estimates.
      PubDate: 2019-04-01
  • A Compactness and Structure Result for a Discrete Multi-well Problem with
           SO ( n ) Symmetry in Arbitrary Dimension
    • Abstract: Abstract In this note we combine the “spin-argument” from Kitavtsev et al. (Proc R Soc Edinb Sect A Mater 147(5):1041–1089, 2017) and the n-dimensional incompatible, one-well rigidity result from Lauteri and Luckhaus (An energy estimate for dislocation configurations and the emergence of Cosserat-type structures in metal plasticity, 2016), in order to infer a new proof for the compactness of discrete multi-well energies associated with the modelling of surface energies in certain phase transitions. Mathematically, a main novelty here is the reduction of the problem to an incompatible one-well problem. The presented argument is very robust and applies to a number of different physically interesting models, including for instance phase transformations in shape-memory materials but also anti-ferromagnetic transformations or related transitions with an “internal” microstructure on smaller scales.
      PubDate: 2019-04-01
  • Elliptic Operators with Honeycomb Symmetry: Dirac Points, Edge States and
           Applications to Photonic Graphene
    • Abstract: Abstract Consider electromagnetic waves in two-dimensional honeycomb structured media, whose constitutive laws have the symmetries of a hexagonal tiling of the plane. The properties of transverse electric polarized waves are determined by the spectral properties of the elliptic operator \({\mathcal{L}^{A}=-\nabla_{\bf x}\cdot A({\bf x}) \nabla_{\bf x}}\) , where A(x) is \({{\Lambda}_h}\) -periodic ( \({{\Lambda}_h}\) denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, A(x) is \({\mathcal{P}\mathcal{C}}\) -invariant ( \({A({\bf x})=\overline{A(-{\bf x})}}\) ) and \({120^\circ}\) rotationally invariant ( \({A(R^*{\bf x})=R^*A({\bf x})R}\) , where R is a \({120^\circ}\) rotation in the plane). A summary of our results is as follows: (a) For generic honeycomb structured media, the band structure of \({\mathcal{L}^{A}}\) has Dirac points, i.e. conical intersections between two adjacent Floquet–Bloch dispersion surfaces; (b) Initial data of wave-packet type, which are spectrally concentrated about a Dirac point, give rise to solutions of the time-dependent Maxwell equations whose wave-envelope, on long time scales, is governed by an effective two-dimensional time-dependent system of massless Dirac equations; (c) Dirac points are unstable to arbitrary small perturbations which break either \({\mathcal{C}}\) (complex-conjugation) symmetry or \({\mathcal{P}}\) (inversion) symmetry; (d) The introduction through small and slow variations of a domain wall across a line-defect gives rise to the bifurcation from Dirac points of highly robust (topologically protected) edge states. These are time-harmonic solutions of Maxwell’s equations which are propagating parallel to the line-defect and spatially localized transverse to it. The transverse localization and strong robustness to perturbation of these edge states is rooted in the protected zero mode of a one-dimensional effective Dirac operator with spatially varying mass term; (e) These results imply the existence of unidirectional propagating edge states for two classes of time-reversal invariant media in which \({\mathcal{C}}\) symmetry is broken: magneto-optic media and bi-anisotropic media.
      PubDate: 2019-04-01
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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