Optimal gradient estimates for multi-phase integrals

We prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems

Elucidation of the disulfide folding pathway of hirudin by a topology-based approach

A theoretical model for the folding of proteins containing disulfide bonds is introduced. The model exploits the knowledge of the native state to favour the progressive establishment of native interactions. At variance with traditional approaches based on native topology, not all native bonds are treated in the same way; in particular, a suitable energy term is introduced to account for the special strength of disulfide bonds (irrespective of whether they are native or not) as well as their ability to undergo intra-molecular reshuffling. The model thus possesses the minimal ingredients necessary to investigated the much debated issue of whether the re-folding process occurs through partially structured intermediates with native or non-native disulfide bonds. This strategy is applied to a context of particular interest, the re-folding process of Hirudin, a thrombin-specific protease inhibitor, for which conflicting folding pathways have been proposed. We show that the only two parameters in the model (temperature and disulfide strength) can be tuned to reproduce well a set of experimental transitions between species with different number of formed disulfide. This model is then used to provide a characterisation of the folding process and a detailed description of the species involved in the rate-limiting step of Hirudin refolding.Comment: 14 pages, 9 figure

Spectral properties and infrared absorption in manganites

Within a recently proposed variational approach it has been shown that, in $La_{1-x}A_xMnO_3$ perovskites with $0<x<0.5$, near the metal-insulator transition, the combined effect of the magnetic and electron-phonon interactions pushes the system toward a regime of two coexisting phases: a low electron density one made by itinerant large polarons forming ferromagnetic domains and a high electron density one made by localized small polarons giving rise to paramagnetic or antiferromagnetic domains depending on temperature. Employing the above-mentioned variational scheme, in this paper spectral and optical properties of manganites are derived for $x=0.3$ at different temperatures. It is found that the phase separation regime induces a robust pseudogap in the excitation spectrum of the system. Then the conductivity spectra are characterized by a transfer of spectral weight from high to low energies, as the temperature $T$ decreases. In the metallic ferromagnetic phase, at low $T$ two types of infrared absorption come out: a Drude term and a broad absorption band due respectively to the coherent and incoherent motion of large polarons. The obtained results turn out in good agreement with experiments.Comment: 9 figure

Ballistic transport in one-dimensional loops with Rashba and Dresselhaus spin-orbit coupling

We discuss the combined effect of Rashba and Dresselhaus spin-orbit interactions in polygonal loops formed by quantum wires, when the electron are injected in a node and collected at the opposite one. The conditions that allow perfect localization are found. Furthermore, we investigate the suppression of the Al'tshuler--Aronov--Spivak oscillations that appear, in presence of a magnetic flux, when the electrons are injected and collected at the same node. Finally, we point out that a recent realization of a ballistic spin interferometer can be used to obtain a reliable estimate of the magnitude ratio of the two spin-orbit interactions.\bigskipComment: 6 figure

Lipschitz Bounds and Nonautonomous Integrals

We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems

Ground state features of the Frohlich model

Following the ideas behind the Feynman approach, a variational wave function is proposed for the Fr\"ohlich model. It is shown that it provides, for any value of the electron-phonon coupling constant, an estimate of the polaron ground state energy better than the Feynman method based on path integrals. The mean number of phonons, the average electronic kinetic and interaction energies, the ground state spectral weight and the electron-lattice correlation function are calculated and successfully compared with the best available results.Comment: 6 figure

Idiopathic benign paroxysmal vertigo in children, a migraine precursor.

OBJECTIVES: We describe the case of a young girl in whom transient deafness occurred when her core body temperature rose. METHODS: The patient was referred for a series of audiological and neurologic evaluations performed over time in both afebrile and febrile states, as well as after a stress test (with a treadmill) in which the body temperature rise simulated the febrile state. RESULTS: The patient was found to have a temporary bilateral hearing loss, but had normal distortion product otoacoustic emissions. Moreover, auditory brain stem responses revealed the absence of neural synchrony when her core body temperature increased. CONCLUSIONS: These results are consistent with a temperature-dependent auditory neuropathy, a rare condition in which patients show normal outer hair cell function and abnormal neural function of the eighth cranial nerve. The symptom is reminiscent of Uhthoff's phenomenon, which is described as transient visual loss and is usually observed in multiple sclerosis. This case of temperature-dependent auditory neuropathy is noteworthy because it sheds light on a disorder of which there have been few reports in the literature. We discuss its similarity to Uhthoff's phenomenon

Boundary regularity for manifold constrained p(x)-harmonic maps

We prove partial and full boundary regularity for manifold constrained (Formula presented.) -harmonic maps