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We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…
Detection of scattered light can determine the susceptibility of dielectrics. Such imaging normally holds Rayleigh's limit: details finer than the wavelength of the incident light cannot be determined from the far-field zone. We show that…
The electronic bands of twisted bilayer graphene (TBLG) with a large-period moir\'e superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are…
We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…
Physical properties reflecting valley asymmetry of Landau levels in a biased bilayer graphene under magnetic field are discussed. Within the $4-$band continuum model with Hartree-corrected self-consistent gap and finite damping factor we…
F.-H. Lin studied minimal graphs of the Dirichlet problem in the hyperbolic space and proved that any such minimal graph has the same global regularity as the boundary if the dimension of the minimal graph is even and that there is an…
The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter epsilon that determines the width of the transition layers tends to zero. The double-well…
Let $(M,g)$ be a Riemannian manifold. Choose a pair $(\alpha,H)$ where $\alpha$ is a calibration and $H$ is a calibrated distribution. Using this data we define a 1-parameter family of forms $\alpha_\varepsilon$ and study its adiabatic…
Frames, or lattices consisting of mass points connected by rigid bonds or central force springs, are important model constructs that have applications in such diverse fields as structural engineering, architecture, and materials science.…
We calculate the electronic band structure of ABA-stacked trilayer graphene in the presence of external gates, using a self-consistent Hartree approximation to take account of screening. In the absence of a gate potential, there are…
Aims: In the present work we investigate the nature of the magnetic Rayleigh-Taylor instability at a density interface permeated by an oblique, homogeneous magnetic field in an incompressible limit. Methods: Using the system of linearised…
Inversion asymmetry in bilayer graphene can be tuned by the displacement field. As a result, the band dispersion in biased bilayer graphene acquires flat band regions near the Dirac points along with a non-trivial band geometry. We analyze…
We present a detailed geometric analysis of adiabatic, anisotropic gravitational collapse formulated in a single Painlev\'e-Gullstrand coordinate system that covers both the interior and exterior, thereby eliminating cross-chart matching…
We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing of the…
We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…
This paper makes the following original contributions. First, we develop a unifying framework for testing shape restrictions based on the Wald principle. The test has asymptotic uniform size control and is uniformly consistent. Second, we…
In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Legendre transform and the implicit function theorem, we prove…
We study the error detection problem in $ q $-ary asymmetric channels wherein every input symbol $ x_i $ is mapped to an output symbol $ y_i $ satisfying $ y_i \geq x_i $. A general setting is assumed where the noise vectors are…
We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for…
We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a…