We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

Hypomorphic mutations in DNA-methyltransferase DNMT3B cause majority of the rare disorder Immunodeficiency, Centromere instability and Facial anomalies syndrome cases (ICF1). By unspecified mechanisms, mutant-DNMT3B interferes with lymphoid-specific pathways resulting in immune response defects. Interestingly, recent findings report that DNMT3B shapes intragenic CpG-methylation of highly-transcribed genes. However, how the DNMT3B-dependent epigenetic network modulates transcription and whether ICF1-specific mutations impair this process remains unknown.

Active research in nanotechnology contemplates the use of nanomaterials for environmental engineering applications. However, a primary challenge is understanding the effects of nanomaterial properties on industrial device performance and translating unique nanoscale properties to the macroscale. One emerging example consists of graphene oxide (GO) membranes for separation processes. Thus, here we investigate how individual GO properties can impact GO membrane characteristics and water permeability.

Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space.

We use highly resolved numerical simulations to study turbulent Rayleigh-Benard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr = 1 and Ra = [4 x 10(6), 3 x 10(9)]. By varying the wavelength. at a fixed amplitude, we find an optimal wavelength lambda(opt) for which the Nusselt-Rayleigh scaling relation is (Nu - 1 proportional to Ra-0.483), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech.

Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition.

In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries.

Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows.

It is commonly agreed that the most challenging problems in modern science and engineering involve the concurrent and nonlinear interaction of multiple phenomena, acting on a broad and disparate spectrum of scales in space and time. It is also understood that such phenomena lie at the interface between different disciplines, such as physics, chemistry, material science and biology. The multiscale and multi-level nature of these problems commands a paradigm shift in the way they need to be handled, both conceptually and in terms of the corresponding problem-solving computational tools

Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. In the present work, in the context of general finite frames, we derive an oracle expression for the mean quadratic risk of a linear diagonal de-noising procedure which immediately yields the optimal linear diagonal estimator. Moreover, we obtain an expression for an unbiased estimator of the risk of any smooth shrinkage rule.