Numerical methods for multiscale transport equations and application to two-phase porous media flow

We discuss numerical methods for linear and nonlinear transport equations with multiscale velocity fields. These methods are themselves multiscaled in nature in the sense that they use macro and micro grids, multiscale test functions. We demonstrate the efficiency of these methods and apply them to two-phase flow in heterogeneous porous media.     

Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs

We present a general strategy for proving ergodicity for stochastically forced nonlinear dissipative PDEs. It consists of two main steps. The first step is the reduction to a finite dimensional Gibbsian dynamics of the low modes. The second step is to prove the equivalence between measures induced by different past histories using Girsanov theorem. As applications, we prove ergodicity for Ginzburg–Landau, Kuramoto–Sivashinsky and Cahn–Hilliard equations with stochastic forcing.     

Projection method III: Spatial discretization on the staggered grid

In E & Liu (SIAM J Numer. Anal., 1995), we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous (we call this the semi-discrete case). In this paper, we address similar questions for the fully discrete case when the spatial variables are discretized using a staggered grid. We prove that the numerical solution in velocity has full accuracy up to the boundary, despite the fact that there are numerical boundary layers present in the semi-discrete solutions.

     

Adaptive minimum action method for the study of rare events

An adaptive minimum action method is proposed for computing the most probable transition paths between stable equilibria in metastable systems that do not necessarily have an underlying energy function, by minimizing the action functional associated with such transition paths. This new algorithm uses the moving mesh strategy to adaptively adjust the grid points over the time interval of transition. Numerical examples are presented to demonstrate the efficiency of the adaptive minimum action method.     

Food Waste Fermentation to Fumaric Acid by <Emphasis Type="Italic">Rhizopus arrhizus RH7-13</Emphasis>

Fumaric acid as a four-carbon unsaturated dicarboxylic acid is widely used in the food and chemical industries. Food waste (FW), rich in carbohydrates and protein, is a promising potential feedstock for renewable bio-based chemicals. In this research, we investigated the capability of Rhizopus arrhizus RH7-13 in producing fumaric acid from FW. The liquid fraction of the FW (L-FW) was proven to be the best seed culture medium in our research. When it was however used to be fermentation medium, the yield of fumaric acid reached 32.68 g/L, at a volumetric production of 0.34 g/L h. The solid fraction of FW mixed with water (S-FW) could also be used as fermentation medium when a certain amount of glucose was added, and the yield of fumaric acid reached 31.26 g/L. The results indicated that both fractions of FW could be well utilized in fermentation process and it could replace a part of common carbon, nitrogen, and nutrient. The process has an application potential since reducing the costs of raw materials.     

Poly(2-Oxazoline)-Based Functional Peptide Mimics: Eradicating MRSA Infections and Persisters while Alleviating Antimicrobial Resistance

Peptides have important biological functions. However, their susceptibility to proteolysis limits their applications. We demonstrated here for the first time, that poly(2-oxazoline) (POX) can work as a functional mimic of peptides. POX-based glycine pseudopeptides, a host defense peptide mimic, had potent activities against methicillin-resistant S. aureus, which causes formidable infections. The POX mimic showed potent activity against persisters that are highly resistant to antibiotics. S. aureus did not develop resistance to POX owning to the reactive oxygen species related antimicrobial mechanism. POX-treated S. aureus is sensitive to common antibiotics, demonstrating no observable antimicrobial pressure or cross-resistance in using antimicrobial POX. This study highlights POX as a new type of functional mimic of peptides and opens new avenues in designing and exploring peptide mimetics for biological functions and applications.     

BN-Embedded Polycyclic Aromatic Hydrocarbon Oligomers: Synthesis,Aromaticity, and Reactivity

BN-embedded oligomers with different pairs of BN units were synthesized by electrophilic borylation. Up to four pairs of BN units were incorporated in the large polycyclic aromatic hydrocarbons (PAHs). Their geometric, photophysical, electrochemical, and Lewis acidic properties were investigated by X-ray crystallography, optical spectroscopy, and cyclic voltammetry. The B−N bonds show delocalized double-bond characteristics and the conjugation can be extended through the trans-orientated aromatic azaborine units. Calculations reveal the relatively lower aromaticity for the inner azaborine rings in the BN-embedded PAH oligomers. The frontier orbitals of the longer oligomers are delocalized over the inner aromatic rings. Consequently, the inner moieties of the BN-embedded PAH oligomers are more active than the outer parts. This is confirmed by a simple oxidation reaction, which has significant effects on the aromaticity and the intramolecular charge-transfer interactions.     

The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy–Born Rule

The electronic structure of a smoothly deformed crystal is analyzed for the case when the effective Hamiltonian is a given function of the nuclei by considering the regime when the scale of the deformation is much larger than the lattice parameter. Wannier functions are defined by projecting the Wannier functions for the undeformed crystal to the space spanned by the wave functions of the deformed crystal. The exponential decay of such Wannier functions is proved for the case when the undeformed crystal is an insulator. The celebrated Cauchy–Born rule for crystal lattices is extended to the present situation for electronic structure analysis.     

Layer-by-layer fabrication of an anatase titania multilayer with gradual sponge-like morphology

The fabrication of a functional multilayer system with a gradually hierarchical order formed by individual titania thin films of different porosity is investigated. The porous or sponge-like nanostructures are fabricated using a diblock copolymer assisted sol–gel process. The successive spin-coating of the sol–gel solution onto the silicon substrate deposits a thin polymer nanocomposite film which is transformed to purely anatase titania nanostructures via calcination. In total, this procedure is repeated layer by layer for three times. This layer-by-layer approach is monitored with grazing incidence small-angle X-ray scattering (GISAXS) after each fabrication step. The GISAXS investigation is complemented in real space with a scanning electron microscopy characterization of the respective preparation stages. From the characterization, a porous titania multilayer system with gradually structured levels is clearly identified.     

Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.