Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2018, Volume 110, pp. 32 - 70

We study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated with critical points of the fractional...

Constant nonlocal mean curvature | Delaunay periodic cylinders | MATHEMATICS | MATHEMATICS, APPLIED | MINIMAL-SURFACES | REGULARITY | FLOWS | 35J Partial differential equations of elliptic type | 35B Qualitative properties of solutions | Operadors, teoria dels | 35 Partial differential equations | Classificació AMS | Operator theory | 47 Operator theory | 47G Integral, integro-differential, and pseudodifferential operators | Equacions diferencials el·líptiques | Matemàtiques i estadística | Differential equations, Partial | Àrees temàtiques de la UPC

Constant nonlocal mean curvature | Delaunay periodic cylinders | MATHEMATICS | MATHEMATICS, APPLIED | MINIMAL-SURFACES | REGULARITY | FLOWS | 35J Partial differential equations of elliptic type | 35B Qualitative properties of solutions | Operadors, teoria dels | 35 Partial differential equations | Classificació AMS | Operator theory | 47 Operator theory | 47G Integral, integro-differential, and pseudodifferential operators | Equacions diferencials el·líptiques | Matemàtiques i estadística | Differential equations, Partial | Àrees temàtiques de la UPC

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 01/2013, Volume 12, Issue 1, pp. 597 - 620

In this article we analyze the minimization of a nonlocal isoperimetric problem (NLIP) posed on the 2-sphere. After establishing the regularity of the free...

Diblock copolymer | Global minimizers | Gamma convergence | Nonlocal isoperimetric problem | Phase transition | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | nonlocal isoperimetric problem | diblock copolymer | LAMELLAR SOLUTIONS | CAHN-HILLIARD | LOCAL MINIMIZERS | MATHEMATICS | PHASE | REGULARITY | HYPERSURFACES | SEPARATION | global minimizers | COPOLYMER

Diblock copolymer | Global minimizers | Gamma convergence | Nonlocal isoperimetric problem | Phase transition | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | nonlocal isoperimetric problem | diblock copolymer | LAMELLAR SOLUTIONS | CAHN-HILLIARD | LOCAL MINIMIZERS | MATHEMATICS | PHASE | REGULARITY | HYPERSURFACES | SEPARATION | global minimizers | COPOLYMER

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 1/2009, Volume 69, Issue 6, pp. 1712 - 1738

We consider analytical and numerical aspects of the phase diagram for microphase separation of diblock copolymers. Our approach is variational and is based...

Material concentration | Phase diagrams | Copolymers | Macromolecules | Mathematical constants | Boundary conditions | Curvature | Monomers | Block copolymers | Phase diagram | Modified cahn-hilliard equation | Diblock copolymers | MATHEMATICS, APPLIED | phase diagram | STABILITY | diblock copolymers | CONVERGENCE | modified Cahn-Hilliard equation | MORPHOLOGY | SURFACES | Separation | Computer simulation | Planes | Asymptotic properties | Density functional theory | Mathematical models

Material concentration | Phase diagrams | Copolymers | Macromolecules | Mathematical constants | Boundary conditions | Curvature | Monomers | Block copolymers | Phase diagram | Modified cahn-hilliard equation | Diblock copolymers | MATHEMATICS, APPLIED | phase diagram | STABILITY | diblock copolymers | CONVERGENCE | modified Cahn-Hilliard equation | MORPHOLOGY | SURFACES | Separation | Computer simulation | Planes | Asymptotic properties | Density functional theory | Mathematical models

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 2002, Volume 71, Issue 7, pp. 1611 - 1614

The richness of spatial structures of the diblock copolymer melts is demonstrated by the minimization of a free-energy functional of nonlocal type. The total...

numerical simulation | diblock copolymer | double gyroid | constant mean curvature surface | Diblock copolymer | Numerical simulation | Constant mean curvature surface | Double gyroid | DIBLOCK COPOLYMERS | BLOCK-COPOLYMERS | PHYSICS, MULTIDISCIPLINARY | MICROPHASE SEPARATION

numerical simulation | diblock copolymer | double gyroid | constant mean curvature surface | Diblock copolymer | Numerical simulation | Constant mean curvature surface | Double gyroid | DIBLOCK COPOLYMERS | BLOCK-COPOLYMERS | PHYSICS, MULTIDISCIPLINARY | MICROPHASE SEPARATION

Journal Article

Journal of Differential Geometry, ISSN 0022-040X, 05/2018, Volume 109, Issue 1, pp. 111 - 175

The nonlocal s-fractional minimal surface equation for Sigma = partial derivative E where E is an open set in R-N is given by H-Sigma(s)(p) := integral(RN) chi...

MATHEMATICS | LEVEL SET APPROACH | CONSTANT | REGULARITY | INEQUALITY

MATHEMATICS | LEVEL SET APPROACH | CONSTANT | REGULARITY | INEQUALITY

Journal Article

Foundations of Physics, ISSN 0015-9018, 2/2014, Volume 44, Issue 2, pp. 213 - 233

I review a class of nonlocally modified gravity models which were proposed to explain the current phase of cosmic acceleration without dark energy. Among the...

History and Philosophical Foundations of Physics | Philosophy of Science | Nonlocal | Mechanics | Quantum Physics | Dark energy | Statistical Physics, Dynamical Systems and Complexity | Modified gravity | Classical and Quantum Gravitation, Relativity Theory | Physics | SCALAR-TENSOR | COSMOLOGICAL CONSTANT | PHYSICS, MULTIDISCIPLINARY | FIELD | NEWTONIAN DYNAMICS | LAMBDA | GRAVITATIONAL BACK-REACTION | CURVED-SPACETIME | EXPECTATION VALUE FORMALISM | DARK ENERGY CONSTRAINTS | Influence | Research | Quantum theory | Acceleration (Mechanics) | Gravity

History and Philosophical Foundations of Physics | Philosophy of Science | Nonlocal | Mechanics | Quantum Physics | Dark energy | Statistical Physics, Dynamical Systems and Complexity | Modified gravity | Classical and Quantum Gravitation, Relativity Theory | Physics | SCALAR-TENSOR | COSMOLOGICAL CONSTANT | PHYSICS, MULTIDISCIPLINARY | FIELD | NEWTONIAN DYNAMICS | LAMBDA | GRAVITATIONAL BACK-REACTION | CURVED-SPACETIME | EXPECTATION VALUE FORMALISM | DARK ENERGY CONSTRAINTS | Influence | Research | Quantum theory | Acceleration (Mechanics) | Gravity

Journal Article

The European Physical Journal C, ISSN 1434-6044, 9/2018, Volume 78, Issue 9, pp. 1 - 13

We study cosmological solutions in nonlocal teleparallel gravity or f(T) theory, where T is the torsion scalar in teleparallel gravity. This is a natural...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | SYMMETRY | COSMOLOGICAL CONSTANT | GENERAL-RELATIVITY | MODELS | STABILITY | DARK ENERGY | DYNAMICS | REPRESENTATION | BARYON ACOUSTIC-OSCILLATIONS | INFLATIONARY UNIVERSE | PHYSICS, PARTICLES & FIELDS | Gravitation | Dark energy | Dynamical systems | Spacetime | Relativity | Dynamic stability

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | SYMMETRY | COSMOLOGICAL CONSTANT | GENERAL-RELATIVITY | MODELS | STABILITY | DARK ENERGY | DYNAMICS | REPRESENTATION | BARYON ACOUSTIC-OSCILLATIONS | INFLATIONARY UNIVERSE | PHYSICS, PARTICLES & FIELDS | Gravitation | Dark energy | Dynamical systems | Spacetime | Relativity | Dynamic stability

Journal Article

Canadian Journal of Physics, ISSN 0008-4204, 03/2014, Volume 93, Issue 2, pp. 242 - 249

I discuss relativistic extensions of MOND in which the metric couples normally to matter. I argue that MOND might be a residual effect from the vacuum...

ENERGY | COSMOLOGICAL CONSTANT | MODELS | PHYSICS, MULTIDISCIPLINARY | MODIFIED NEWTONIAN DYNAMICS | VACUUM POLARIZATION | FIELD | MASS | DARK-MATTER | STATE | MODIFIED GRAVITY | Newton's laws of motion | Analysis | Gravity

ENERGY | COSMOLOGICAL CONSTANT | MODELS | PHYSICS, MULTIDISCIPLINARY | MODIFIED NEWTONIAN DYNAMICS | VACUUM POLARIZATION | FIELD | MASS | DARK-MATTER | STATE | MODIFIED GRAVITY | Newton's laws of motion | Analysis | Gravity

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 01/1998, Volume 108, Issue 3, pp. 1148 - 1156

Expressions for the surface tension sigma, Tolman length delta, and for the rigidity constants k and (k) over bar of a curved liquid-vapor interface in mean...

DROPS | MOLECULAR-DYNAMICS | CONSTANTS | LIQUID-VAPOR INTERFACE | LANDAU THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

DROPS | MOLECULAR-DYNAMICS | CONSTANTS | LIQUID-VAPOR INTERFACE | LANDAU THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 02/2015, Volume 30, Issue 3n04, p. 1540003

This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the...

Nonlocal effective action | Schwinger-Keldysh formalism | Dark energy | BACKREACTION | EQUATIONS | CONSTANT | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | dark energy | BACK-REACTION | ASTRONOMY & ASTROPHYSICS | CONSEQUENCES | FORMALISM | SCHWINGER-DEWITT TECHNIQUE | HEAT KERNEL | COVARIANT PERTURBATION-THEORY | PHYSICS, PARTICLES & FIELDS

Nonlocal effective action | Schwinger-Keldysh formalism | Dark energy | BACKREACTION | EQUATIONS | CONSTANT | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | dark energy | BACK-REACTION | ASTRONOMY & ASTROPHYSICS | CONSEQUENCES | FORMALISM | SCHWINGER-DEWITT TECHNIQUE | HEAT KERNEL | COVARIANT PERTURBATION-THEORY | PHYSICS, PARTICLES & FIELDS

Journal Article

The European Physical Journal C, ISSN 1434-6044, 4/2018, Volume 78, Issue 4, pp. 1 - 10

We have recently constructed a manifestly local formulation of a nonlocal approach to the cosmological constant problem which can treat with quantum effects...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | FLATNESS | INFLATIONARY UNIVERSE | HORIZON | PHYSICS, PARTICLES & FIELDS | Gravity | Gravitational fields | Cosmological constant | Universe | Gravitational effects | Acceleration | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology | Astrophysics | High Energy Physics - Theory

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | FLATNESS | INFLATIONARY UNIVERSE | HORIZON | PHYSICS, PARTICLES & FIELDS | Gravity | Gravitational fields | Cosmological constant | Universe | Gravitational effects | Acceleration | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology | Astrophysics | High Energy Physics - Theory

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2017, Volume 56, Issue 1, pp. 1 - 46

The fractional Yamabe problem, proposed by González and Qing (Analysis PDE 6:1535–1576, 2013), is a geometric question which concerns the existence of metrics...

Secondary 58J05 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35B44 | Mathematics | Primary 35R11 | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | NIRENBERG PROBLEM | CONFORMAL DEFORMATION | EQUATIONS | BLOW-UP PHENOMENA | BOUNDARY | SCALAR-FLAT METRICS | EXTENSION PROBLEM | ELLIPTIC PROBLEM | RIEMANNIAN-MANIFOLDS

Secondary 58J05 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35B44 | Mathematics | Primary 35R11 | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | NIRENBERG PROBLEM | CONFORMAL DEFORMATION | EQUATIONS | BLOW-UP PHENOMENA | BOUNDARY | SCALAR-FLAT METRICS | EXTENSION PROBLEM | ELLIPTIC PROBLEM | RIEMANNIAN-MANIFOLDS

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 09/2014, Volume 29, Issue 24, p. 1450134

The WZNW and string models are considered in terms of the initial and invariant chiral currents assuming that the internal and external torsions coincide...

Hydrodynamic chain | WZNW model | Poisson bracket | Hamiltonian structure | String model | Chiral currents | Casimir operator | Hydrodynamic type equation | SPACES | ALGEBRA | NONLOCAL HAMILTONIAN OPERATORS | TOPOLOGICAL FIELD-THEORY | CHARGES | PHYSICS, NUCLEAR | chiral currents | SYMMETRY | hydrodynamic type equation | string model | hydrodynamic chain | PHYSICS, PARTICLES & FIELDS

Hydrodynamic chain | WZNW model | Poisson bracket | Hamiltonian structure | String model | Chiral currents | Casimir operator | Hydrodynamic type equation | SPACES | ALGEBRA | NONLOCAL HAMILTONIAN OPERATORS | TOPOLOGICAL FIELD-THEORY | CHARGES | PHYSICS, NUCLEAR | chiral currents | SYMMETRY | hydrodynamic type equation | string model | hydrodynamic chain | PHYSICS, PARTICLES & FIELDS

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 06/2018, Volume 43, Issue 6, pp. 859 - 892

We consider linear and non-linear boundary value problems associated to the fractional Hardy-Schrödinger operator on domains of containing the singularity 0,...

Critical exponent | nonlocal operators | Hardy inequalities | fractional Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POSITIVE SOLUTIONS | EQUATIONS | SHARP CONSTANTS | SOBOLEV | Operators (mathematics) | Domains | Eigenvalues | Boundary value problems | Linear equations | Analysis of PDEs | Mathematics

Critical exponent | nonlocal operators | Hardy inequalities | fractional Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POSITIVE SOLUTIONS | EQUATIONS | SHARP CONSTANTS | SOBOLEV | Operators (mathematics) | Domains | Eigenvalues | Boundary value problems | Linear equations | Analysis of PDEs | Mathematics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2017, Volume 58, Issue 2, p. 22701

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian H = T + V into a geodesic Hamiltonian T with one additional degree of...

SCHRODINGER-EQUATIONS | NONCONSTANT CURVATURE | KILLING TENSORS | CONSTANT-CURVATURE | SMORODINSKY-WINTERNITZ POTENTIALS | HYPERBOLIC PLANE | EUCLIDEAN-SPACE | PHYSICS, MATHEMATICAL | VARIABLE SEPARATION | POSITION-DEPENDENT MASS | DYNAMICAL TRAJECTORIES | Hamiltonian functions | Formalism | Euclidean geometry

SCHRODINGER-EQUATIONS | NONCONSTANT CURVATURE | KILLING TENSORS | CONSTANT-CURVATURE | SMORODINSKY-WINTERNITZ POTENTIALS | HYPERBOLIC PLANE | EUCLIDEAN-SPACE | PHYSICS, MATHEMATICAL | VARIABLE SEPARATION | POSITION-DEPENDENT MASS | DYNAMICAL TRAJECTORIES | Hamiltonian functions | Formalism | Euclidean geometry

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 7/2018, Volume 172, Issue 2, pp. 458 - 476

We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from ($$\text {n}+1$$ n+1...

Volume preserving mean curvature flow | Submanifold | Constant mean curvature surface | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Effective dynamic | Quantum Physics | Adiabatic dynamic | Physics | Mean curvature flow | Statistical Physics and Dynamical Systems | SPHERES | STABILITY | LIMIT | PHYSICS, MATHEMATICAL | MOTION | CONVERGENCE | MAP

Volume preserving mean curvature flow | Submanifold | Constant mean curvature surface | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Effective dynamic | Quantum Physics | Adiabatic dynamic | Physics | Mean curvature flow | Statistical Physics and Dynamical Systems | SPHERES | STABILITY | LIMIT | PHYSICS, MATHEMATICAL | MOTION | CONVERGENCE | MAP

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 12/2017, Volume 2017, Issue 12, pp. 1 - 51

We study recently proposed chiral higher spin theories — cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that...

Integrable Field Theories | Higher Spin Gravity | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | MASSLESS HIGHER SPINS | EQUATIONS | KAC-MOODY ALGEBRA | GENERATING FUNCTION | HIDDEN-SYMMETRY ALGEBRA | GAUGE-FIELDS | CONSERVATION-LAWS | INTERACTION VERTICES | CUBIC INTERACTION TERMS | NONLOCAL CHARGES | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Gravity | Amplitudes | Deformation | Mathematical analysis | Color | Constants | Equations of motion | Physics - High Energy Physics - Theory | High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Lattice

Integrable Field Theories | Higher Spin Gravity | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | MASSLESS HIGHER SPINS | EQUATIONS | KAC-MOODY ALGEBRA | GENERATING FUNCTION | HIDDEN-SYMMETRY ALGEBRA | GAUGE-FIELDS | CONSERVATION-LAWS | INTERACTION VERTICES | CUBIC INTERACTION TERMS | NONLOCAL CHARGES | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Gravity | Amplitudes | Deformation | Mathematical analysis | Color | Constants | Equations of motion | Physics - High Energy Physics - Theory | High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Lattice

Journal Article

Entropy, ISSN 1099-4300, 2015, Volume 17, Issue 4, pp. 1916 - 1935

This study describes the structure of an inhomogeneous fluid of one or several components that forms a spherical interface. Using the stress tensor of...

Density functional theory | Pressure tensor | Interfacial properties | Density profile | CURVED INTERFACES | MICROSCOPIC EXPRESSIONS | FLUID | PHYSICS, MULTIDISCIPLINARY | STRESS TENSOR | VAPOR INTERFACE | SPONTANEOUS CURVATURE | NONUNIFORM | SURFACE-TENSION | SPHERICAL INTERFACE | INTERFACIAL BENDING CONSTANTS | Fluids | Liquids | Fluid dynamics | Mathematical analysis | Fluid flow | Nanostructure | Entropy | Density | density profile | interfacial properties | pressure tensor | density functional theory

Density functional theory | Pressure tensor | Interfacial properties | Density profile | CURVED INTERFACES | MICROSCOPIC EXPRESSIONS | FLUID | PHYSICS, MULTIDISCIPLINARY | STRESS TENSOR | VAPOR INTERFACE | SPONTANEOUS CURVATURE | NONUNIFORM | SURFACE-TENSION | SPHERICAL INTERFACE | INTERFACIAL BENDING CONSTANTS | Fluids | Liquids | Fluid dynamics | Mathematical analysis | Fluid flow | Nanostructure | Entropy | Density | density profile | interfacial properties | pressure tensor | density functional theory

Journal Article