Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 10/2016, Volume 222, Issue 1, pp. 427 - 450

We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | DEFECTS | MECHANICS | HARMONIC MAPS | MINIMIZATION | REGULARITY | STABILITY | LIQUID-CRYSTAL | Point defects | Saturn | Colloids | Eigenvalues | Configurations | Nematic crystals | Liquid crystals | Anchoring | Constraining | Exchange | Axisymmetric | Saturn rings | Analysis of PDEs | Mathematics

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | DEFECTS | MECHANICS | HARMONIC MAPS | MINIMIZATION | REGULARITY | STABILITY | LIQUID-CRYSTAL | Point defects | Saturn | Colloids | Eigenvalues | Configurations | Nematic crystals | Liquid crystals | Anchoring | Constraining | Exchange | Axisymmetric | Saturn rings | Analysis of PDEs | Mathematics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 11/2015, Volume 56, Issue 11

We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and...

CRITICAL-FIELD | SR2RUO4 | VORTICES | GINZBURG-LANDAU EQUATION | FERROMAGNETIC INTERACTIONS | MODEL | PHYSICS, MATHEMATICAL | LATTICE | Potential energy | Domains | Nonlinear equations | Partial differential equations | Asymptotic properties | Mathematical analysis | Vortices | Differential equations | Wave functions | Analysis of PDEs | Mathematics

CRITICAL-FIELD | SR2RUO4 | VORTICES | GINZBURG-LANDAU EQUATION | FERROMAGNETIC INTERACTIONS | MODEL | PHYSICS, MATHEMATICAL | LATTICE | Potential energy | Domains | Nonlinear equations | Partial differential equations | Asymptotic properties | Mathematical analysis | Vortices | Differential equations | Wave functions | Analysis of PDEs | Mathematics

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 8/2018, Volume 28, Issue 4, pp. 1443 - 1465

We consider a nematic liquid crystal occupying the exterior region in $${\mathbb {R}}^3$$ R3 outside of a spherical particle, with radial strong anchoring....

Partial differential equations | 35J50 | Line defects | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q56 | Mathematics | Calculus of variations | Liquid crystals | POINT-DEFECTS | MATHEMATICS, APPLIED | MECHANICS | STABILITY | DE-GENNES ENERGY | MODEL | PHYSICS, MATHEMATICAL | MINIMIZERS | Saturn (Planet) | Mathematics - Analysis of PDEs | Analysis of PDEs

Partial differential equations | 35J50 | Line defects | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q56 | Mathematics | Calculus of variations | Liquid crystals | POINT-DEFECTS | MATHEMATICS, APPLIED | MECHANICS | STABILITY | DE-GENNES ENERGY | MODEL | PHYSICS, MATHEMATICAL | MINIMIZERS | Saturn (Planet) | Mathematics - Analysis of PDEs | Analysis of PDEs

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 11/2015, Volume 56, Issue 11, p. 1

We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions,...

Qualitative research | Superconductors | Partial differential equations | Vortices | Symmetry

Qualitative research | Superconductors | Partial differential equations | Vortices | Symmetry

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10, p. 1

We prove that both the liquid drop model in R3 with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsacker (TFDW) model attain their...

Molecules | Attraction | Decay rate | Atoms & subatomic particles | Mathematical models

Molecules | Attraction | Decay rate | Atoms & subatomic particles | Mathematical models

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10

We prove that both the liquid drop model in R3 with an attractive background nucleus and theThomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their...

Attraction | Decay rate

Attraction | Decay rate

Journal Article

Physical Review E, ISSN 2470-0045, 01/2016, Volume 93, Issue 1, p. 012705

We derive an analytical formula for the Saturn-ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we...

TOPOLOGICAL COLLOIDS | DISPERSIONS | PARTICLES | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | LIQUID-CRYSTALS

TOPOLOGICAL COLLOIDS | DISPERSIONS | PARTICLES | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | LIQUID-CRYSTALS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10, p. 103503

We prove that both the liquid drop model in R 3 with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their...

ATOMS | THOMAS-FERMI | MOND | PHYSICS, MATHEMATICAL

ATOMS | THOMAS-FERMI | MOND | PHYSICS, MATHEMATICAL

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2015, Volume 215, Issue 2, pp. 579 - 610

A thorough study of domain wall solutions in coupled Gross–Pitaevskii equations on the real line is carried out including existence of these solutions; their...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITONS | MODULATIONAL INSTABILITY | POTENTIALS | ORBITAL STABILITY | Stability | Mathematical analysis | Bose-Einstein condensates | Domain walls | Spectral lines | Nonlinearity | Joining | Mathematical models | Mathematics - Analysis of PDEs

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITONS | MODULATIONAL INSTABILITY | POTENTIALS | ORBITAL STABILITY | Stability | Mathematical analysis | Bose-Einstein condensates | Domain walls | Spectral lines | Nonlinearity | Joining | Mathematical models | Mathematics - Analysis of PDEs

Journal Article

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, ISSN 1534-0392, 01/2020, Volume 19, Issue 1, pp. 175 - 202

We address small volume-fraction asymptotic properties of a non-local isoperimetric functional with a confinement term, derived as the sharp interface limit of...

MATHEMATICS, APPLIED | NONEXISTENCE | PARTICLES | LIMIT | COPOLYMERS | uniformly charged liquid | MATHEMATICS | phase separation | confinement | MINIMALITY | self-assembly of diblock copolymers | Gamma-convergence | Nonlocal isoperimetric problem

MATHEMATICS, APPLIED | NONEXISTENCE | PARTICLES | LIMIT | COPOLYMERS | uniformly charged liquid | MATHEMATICS | phase separation | confinement | MINIMALITY | self-assembly of diblock copolymers | Gamma-convergence | Nonlocal isoperimetric problem

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 05/2019, Volume 21, Issue 3, p. 1850022

We consider a variant of Gamow’s liquid drop model, with a general repulsive Riesz kernel and a long-range attractive background potential with weight Z . The...

background potential | droplet breakup | Liquid drop model | generalized minimizer | concentration-compactness method | nonlocal isoperimetric problem | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | NONEXISTENCE | MATHEMATICS | MINIMALITY | MOND | ISOPERIMETRIC PROBLEM

background potential | droplet breakup | Liquid drop model | generalized minimizer | concentration-compactness method | nonlocal isoperimetric problem | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | NONEXISTENCE | MATHEMATICS | MINIMALITY | MOND | ISOPERIMETRIC PROBLEM

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2013, Volume 255, Issue 10, pp. 3564 - 3591

We study Ginzburg–Landau equations for a complex vector order parameter . We consider symmetric vortex solutions in the plane , , with given degrees , and...

Elliptic equations and systems | Calculus of variations | Vortices | Superconductivity | MATHEMATICS | VORTEX SOLUTIONS | EQUATIONS | FRACTIONAL DEGREE VORTICES | MODEL

Elliptic equations and systems | Calculus of variations | Vortices | Superconductivity | MATHEMATICS | VORTEX SOLUTIONS | EQUATIONS | FRACTIONAL DEGREE VORTICES | MODEL

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2014, Volume 267, Issue 6, pp. 1751 - 1777

We study Ginzburg–Landau equations for a complex vector order parameter . We consider the Dirichlet problem in the disk in with a symmetric, degree-one...

Elliptic equations and systems | Calculus of variations | Vortices | Superconductivity | MATHEMATICS | EQUATION

Elliptic equations and systems | Calculus of variations | Vortices | Superconductivity | MATHEMATICS | EQUATION

Journal Article

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Vortices and pinning effects for the Ginzburg‐Landau model in multiply connected domains

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 01/2006, Volume 59, Issue 1, pp. 36 - 70

We consider the two‐dimensional Ginzburg‐Landau model with magnetic field for a superconductor with a multiply connected cross section. We study energy...

Journal Article

15.
Full Text
A Degenerate Isoperimetric Problem and Traveling Waves to a Bistable Hamiltonian System

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 02/2017, Volume 70, Issue 2, pp. 340 - 377

We analyze a nonstandard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain...

DENSITY | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | DIFFUSION-SYSTEMS | NONCONVEX VARIATIONAL-PROBLEMS

DENSITY | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | DIFFUSION-SYSTEMS | NONCONVEX VARIATIONAL-PROBLEMS

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2012, Volume 61, Issue 5, pp. 1861 - 1909

We study the structure of vortex solutions in a Ginzburg-Landau system for two complex-valued order parameters. We consider the Dirichlet problem in the disk...

Boundary value problems | Energy | Infinity | Differential equations | Uniqueness | Eigenvalues | Boundary conditions | Ground state | Eigenfunctions | Dirichlet problem | Partial differential equations | Bifurcations | Calculus of variations | MATHEMATICS | bifurcations | calculus of variations | partial differential equations | FRACTIONAL DEGREE VORTICES | MODEL | EQUATION | Analysis of PDEs | Mathematics

Boundary value problems | Energy | Infinity | Differential equations | Uniqueness | Eigenvalues | Boundary conditions | Ground state | Eigenfunctions | Dirichlet problem | Partial differential equations | Bifurcations | Calculus of variations | MATHEMATICS | bifurcations | calculus of variations | partial differential equations | FRACTIONAL DEGREE VORTICES | MODEL | EQUATION | Analysis of PDEs | Mathematics

Journal Article

17.
Full Text
Giant Vortex and the Breakdown of Strong Pinning in a Rotating Bose-Einstein Condensate

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 11/2005, Volume 178, Issue 2, pp. 247 - 286

We consider a two-dimensional model for a rotating Bose-Einstein condensate (BEC) in an anharmonic trap. The special shape of the trapping potential, negative...

Mechanics | Fluids | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | PART-I | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SUPERCONDUCTIVITY | GINZBURG-LANDAU ENERGY | CRITICAL MAGNETIC-FIELD | EQUATIONS | MODEL | MINIMIZERS | ASYMPTOTIC-BEHAVIOR

Mechanics | Fluids | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | PART-I | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SUPERCONDUCTIVITY | GINZBURG-LANDAU ENERGY | CRITICAL MAGNETIC-FIELD | EQUATIONS | MODEL | MINIMIZERS | ASYMPTOTIC-BEHAVIOR

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 06/2015, Volume 119, pp. 74 - 97

We study the weak anchoring condition for nematic liquid crystals in the context of the Landau–De Gennes model. We restrict our attention to two dimensional...

Liquid crystals | Landau–de Gennes | Landau-de Gennes | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | DEFECTS | LOWER BOUNDS | MINIMIZATION | Crystal defects | Mathematical models | Droplets | Boundaries | Two dimensional | Nematic | Anchoring

Liquid crystals | Landau–de Gennes | Landau-de Gennes | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | DEFECTS | LOWER BOUNDS | MINIMIZATION | Crystal defects | Mathematical models | Droplets | Boundaries | Two dimensional | Nematic | Anchoring

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 2/2012, Volume 310, Issue 1, pp. 237 - 266

We study minimizers of the Lawrence–Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LAYERED SUPERCONDUCTORS | PHYSICS, MATHEMATICAL | VORTICES | Superconductors | Magnetic fields | Anisotropy | Analysis | Classical Physics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LAYERED SUPERCONDUCTORS | PHYSICS, MATHEMATICAL | VORTICES | Superconductors | Magnetic fields | Anisotropy | Analysis | Classical Physics

Journal Article

Interfaces and Free Boundaries, ISSN 1463-9963, 2016, Volume 18, Issue 2, pp. 263 - 289

We identify the Gamma-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase...

Nanoparticles | γ -convergence | Self-assembly | Isoperimetric problem | Phase separation | Block copolymers | block copolymers | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | LIQUID-DROPS | MINIMIZERS | NONLOCAL ISOPERIMETRIC PROBLEM | MATHEMATICS | self-assembly | phase separation | DIBLOCK COPOLYMER/PARTICLE COMPOSITES | I-LIMIT | MEAN-CURVATURE | isoperimetric problem | VARIATIONAL-PROBLEMS | Gamma-convergence | 2 DIMENSIONS | SURFACES

Nanoparticles | γ -convergence | Self-assembly | Isoperimetric problem | Phase separation | Block copolymers | block copolymers | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | LIQUID-DROPS | MINIMIZERS | NONLOCAL ISOPERIMETRIC PROBLEM | MATHEMATICS | self-assembly | phase separation | DIBLOCK COPOLYMER/PARTICLE COMPOSITES | I-LIMIT | MEAN-CURVATURE | isoperimetric problem | VARIATIONAL-PROBLEMS | Gamma-convergence | 2 DIMENSIONS | SURFACES

Journal Article

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