Browsing Analysis of Partial Differential Equations (APDE) by Issue Date
Now showing items 1-20 of 266
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Leaky Cell Model of Hard Spheres
Fai, Tomas G.; Taylor, J.M.
; Virga, Epifanio G.; Zheng, Xiaoyu; Palffy-Muhoray, Peter (9-03-20)
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without ... -
Relativistic Hardy Inequalities in Magnetic Fields
Fanelli, L.; Vega, L.; Visciglia, N. (2014-12-31)
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... -
Vortex filament equation for a regular polygon
De la Hoz, F.; Vega, L. (2014-12-31)
In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ... -
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(2015-05-01)The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ... -
The dynamics of vortex filaments with corners
Vega, L. (2015-07-01)
This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon ... -
The Vortex Filament Equation as a Pseudorandom Generator
De la Hoz, F.; Vega, L. (2015-08-01)
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$ X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ... -
The initial value problem for the binormal flow with rough data
Banica, V.; Vega, L. (2015-12-31)
In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ... -
Shell interactions for Dirac operators: On the point spectrum and the confinement
Arrizabalaga, N.; Mas, A.; Vega, L. (2015-12-31)
Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ... -
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0]
Fanelli, L.; Vega, L.; Visciglia, N. (2015-12-31)
[No abstract available] -
An atomistic/continuum coupling method using enriched bases
Chen, J.; García-Cervera, C.J.; Li, X. (2015-12-31)
A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to ... -
A Mean-field model for spin dynamics in multilayered ferromagnetic media
Chen, J.; García-Cervera, C.J.; Yang, X. (2015-12-31)
In this paper, we develop a mean-field model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the ... -
Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions
Chen, J.; García-Cervera, C.J.; Yang, X. (2015-12-31)
In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ... -
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(2016-01-01)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of ... -
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
Ombrosi, S.; Pérez, C. (2016-01-01)
In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2]. -
Inverse scattering for a random potential
(2016-05)In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... -
An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
Arrizabalaga, N.; Mas, A.; Vega, L. (2016-06-01)
In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ... -
Reverse Hölder Property for Strong Weights and General Measures
Luque, T.; Pérez, C.; Rela, E. (2016-06-30)
We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ... -
Quantitative weighted mixed weak-type inequalities for classical operators
Ombrosi, S.; Pérez, C.; Recchi, J. (2016-06-30)
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ... -
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
(2016-06-30)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... -
Borderline Weighted Estimates for Commutators of Singular Integrals
Pérez, C.; Rivera-Ríos, I.P. (2016-07-01)
In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\f ...