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Articles 181 - 196 of 196
Full-Text Articles in Mathematics
Schwinger Pair Creation Of Kaluza-Klein Particles: Pair Creation Without Tunneling, Tamar Friedmann, Herman Verlinde
Schwinger Pair Creation Of Kaluza-Klein Particles: Pair Creation Without Tunneling, Tamar Friedmann, Herman Verlinde
Mathematics Sciences: Faculty Publications
We study Schwinger pair creation of charged Kaluza-Klein (KK) particles from a static KK electric field. We find that the gravitational backreaction of the electric field on the geometry—which is incorporated via the electric KK-Melvin solution—prevents the electrostatic potential from overcoming the rest mass of the KK particles, thus impeding the tunneling mechanism which is often thought of as responsible for the pair creation. However, we find that pair creation still occurs with a finite rate formally similar to the classic Schwinger result, but via an apparently different mechanism, involving a combination of the Unruh effect and vacuum polarization due …
The Aronsson-Euler Equation For Absolutely Minimizing Lipschitz Extensions With Respect To Carnot-Carathéodory Metrics, Thomas Bieske, Luca Capogna
The Aronsson-Euler Equation For Absolutely Minimizing Lipschitz Extensions With Respect To Carnot-Carathéodory Metrics, Thomas Bieske, Luca Capogna
Mathematics Sciences: Faculty Publications
We derive the Euler-Lagrange equation (also known in this setting as the Aronsson-Euler equation) for absolute minimizers of the L ∞ variational problem inf∥∇ 0u∥L∞(Ω), u = g ε Lip(∂Ω) on ∂Ω, where Ω ⊂ G is an open subset of a Carnot group, ∇ 0u denotes the horizontal gradient of u: Ω ℝ R, and the Lipschitz class is defined in relation to the Carnot-Carathéodory metric. In particular, we show that absolute minimizers are infinite harmonic in the viscosity sense. As a corollary we obtain the uniqueness of absolute minimizers in a large class of groups. This result extends …
Distinguishing Numbers For Graphs And Groups, Julianna Tymoczko
Distinguishing Numbers For Graphs And Groups, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
A graph G is distinguished if its vertices are labelled by a map φ: V(G) → {1,2,..., k} so that no non-trivial graph automorphism preserves φ. The distinguishing number of G is the minimum number k necessary for φ to distinguish the graph. It measures the symmetry of the graph. We extend these definitions to an arbitrary group action of Γ on a set X. A labelling φ: X → {1, 2,..., k} is distinguishing if no element of Γ preserves Γ except those which fix each element of X. The distinguishing number of the group action on X is …
Regularity Of Minimizers Of The Calculus Of Variations In Carnot Groups Via Hypoellipticity Of Systems Of Hörmander Type, Luca Capogna, Nicola Garofalo
Regularity Of Minimizers Of The Calculus Of Variations In Carnot Groups Via Hypoellipticity Of Systems Of Hörmander Type, Luca Capogna, Nicola Garofalo
Mathematics Sciences: Faculty Publications
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.
Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang
Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang
Mathematics Sciences: Faculty Publications
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t-3/2. While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.
Planar Minimally Rigid Graphs And Pseudo-Triangulations, Ruth Haas, David Orden, Günter Rote, Francisco Santos, Herman Servatius, Diane Souvaine, Ileana Streinu, Walter Whiteley
Planar Minimally Rigid Graphs And Pseudo-Triangulations, Ruth Haas, David Orden, Günter Rote, Francisco Santos, Herman Servatius, Diane Souvaine, Ileana Streinu, Walter Whiteley
Mathematics Sciences: Faculty Publications
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial constraints. The proofs yield efficient embedding algorithms. They also provide - to the best of our knowledge - the first algorithmically effective result on graph embeddings with oriented matroid constraints other than convexity of faces. These constraints are described by combinatorial pseudo-triangulations, first defined and studied in this paper. Also …
Unification Scale, Proton Decay, And Manifolds Of G2 Holonomy, Tamar Friedmann, Edward Witten
Unification Scale, Proton Decay, And Manifolds Of G2 Holonomy, Tamar Friedmann, Edward Witten
Mathematics Sciences: Faculty Publications
Models of particle physics based on manifolds of G2 holonomy are in most respects much more complicated than other string-derived models, but as we show here they do have one simplification: threshold corrections to grand unification are particularly simple. We compute these corrections, getting completely explicit results in some simple cases. We estimate the relation between Newton’s constant, the GUT scale, and the value of αGUT , and explore the implications for proton decay. In the case of proton decay, there is an interesting mechanism which (relative to four-dimensional SUSY GUT’s) enhances the gauge boson contribution to p → π …
A Dynamical System For Plant Pattern Formation: A Rigorous Analysis, Pau Atela, Christophe Golé, S. Hotton
A Dynamical System For Plant Pattern Formation: A Rigorous Analysis, Pau Atela, Christophe Golé, S. Hotton
Mathematics Sciences: Faculty Publications
We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system, as well as by the structure of their bifurcation diagram. We provide a detailed study of this diagram.
On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann
On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann
Mathematics Sciences: Faculty Publications
We study the moduli space of M-theories compactified on G2 manifolds which are asymptotic to a cone over quotients of S3 × S3. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U (1) factors. Each component smoothly interpolates among supersymmetric gauge theories with different gauge groups.
Lagrangian Systems On Hyperbolic Manifolds, Philip Boyland, Christophe Golé
Lagrangian Systems On Hyperbolic Manifolds, Philip Boyland, Christophe Golé
Mathematics Sciences: Faculty Publications
This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincaré ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and have a variety of approximate speeds. Theorem B gives the existence of a collection of compact invariant sets of the Euler-Lagrange flow that are semiconjugate to the geodesic flow of a hyperbolic metric. These results can be viewed as …
A Version Of A Theorem Of Dahlberg For The Subelliptic Dirichlet Problem, Luca Capogna, Nicola Garofalo, Duy Minh Nhieu
A Version Of A Theorem Of Dahlberg For The Subelliptic Dirichlet Problem, Luca Capogna, Nicola Garofalo, Duy Minh Nhieu
Mathematics Sciences: Faculty Publications
No abstract provided.
A Note On Carnot Geodesics In Nilpotent Lie Groups, Christophe Golé, Ron Karidi
A Note On Carnot Geodesics In Nilpotent Lie Groups, Christophe Golé, Ron Karidi
Mathematics Sciences: Faculty Publications
We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct a group, with a left invariant bracket-generating distribution, for which some Carnot geodecics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves, which we derive (for any Lie group) explicitly in terms of the structure constants. © 1995 Plenum Publishing Corporation.
Optical Hamiltonians And Symplectic Twist Maps, Christophe Golé
Optical Hamiltonians And Symplectic Twist Maps, Christophe Golé
Mathematics Sciences: Faculty Publications
This paper concentrates on optical Hamiltonian systems of T*Tn, i.e., those for which Hpp is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems. The novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system.
Periodic Orbits For Hamiltonian Systems In Cotangent Bundles, Christophe Golé
Periodic Orbits For Hamiltonian Systems In Cotangent Bundles, Christophe Golé
Mathematics Sciences: Faculty Publications
We prove the existence of at least cl(Af) periodic orbits for certain time-dependent Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time-1 map into a product of "symplectic twist maps". A second theorem deals with homotopically non-trivial orbits of negative curvature.
A New Proof Of The Aubry-Mather's Theorem, Christophe Golé
A New Proof Of The Aubry-Mather's Theorem, Christophe Golé
Mathematics Sciences: Faculty Publications
No abstract provided.
Ghost Circles For Twist Maps, Christophe Golé
Ghost Circles For Twist Maps, Christophe Golé
Mathematics Sciences: Faculty Publications
Completely ordered invariant circles are found for the gradient of the energy flow in the state space, containing the critical sets corresponding to the Birkhoff orbits of all rotation number. In particular, these ghost circles contain the Aubry-Mather sets and map-invariant circles as completely critical sets when these exist. We give a criterion for a sequence of rational ghost circles to converge to a completely critical one.