Mathematical models for erosion and the optimal transportation of sediment

We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment

On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Alterations in Brain-Derived Neurotrophic Factor in the Mouse Hippocampus Following Acute but Not Repeated Benzodiazepine Treatment

Benzodiazepines (BZs) are safe drugs for treating anxiety, sleep, and seizure disorders, but their use also results in unwanted effects including memory impairment, abuse, and dependence. The present study aimed to reveal the molecular mechanisms that may contribute to the effects of BZs in the hippocampus (HIP), an area involved in drug-related plasticity, by investigating the regulation of immediate early genes following BZ administration. Previous studies have demonstrated that both brain derived neurotrophic factor (BDNF) and c-Fos contribute to memory- and abuse-related processes that occur within the HIP, and their expression is altered in response to BZ exposure. In the current study, mice received acute or repeated administration of BZs and HIP tissue was analyzed for alterations in BDNF and c-Fos expression. Although no significant changes in BDNF or c-Fos were observed in response to twice-daily intraperitoneal (i.p.) injections of diazepam (10 mg/kg + 5 mg/kg) or zolpidem (ZP; 2.5 mg/kg + 2.5 mg/kg), acute i.p. administration of both triazolam (0.03 mg/kg) and ZP (1.0 mg/kg) decreased BDNF protein levels within the HIP relative to vehicle, without any effect on c-Fos. ZP specifically reduced exon IV-containing BDNF transcripts with a concomitant increase in the association of methyl-CpG binding protein 2 (MeCP2) with BDNF promoter IV, suggesting that MeCP2 activity at this promoter may represent a ZP-specific mechanism for reducing BDNF expression. ZP also increased the association of phosphorylated cAMP response element binding protein (pCREB) with BDNF promoter I. Future work should examine the interaction between ZP and DNA as the cause for altered gene expression in the HIP, given that BZs can enter the nucleus and intercalate into DNA directly

The fundamental gap of simplices

The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in $\R^n$ normalized to have unit diameter, the difference between the first two Dirichlet eigenvalues of the Laplacian is bounded below by that of the interval. In this work, we focus on the moduli spaces of simplices in all dimensions, and later specialize to the moduli space of Euclidean triangles. Our first theorem is a compactness result for the gap function on the moduli space of simplices in any dimension. Our second main result verifies a recent conjecture of Antunes-Freitas: for any Euclidean triangle normalized to have unit diameter, the fundamental gap is uniquely minimized by the equilateral triangle.Comment: Final version, Journal ref adde

Battery-Flywheel Hybrid Electric Power System for Near Term Application. Volume 2. System Design.

This is the second of two volumes which document the result of an investigation of Battery-Flywheel Power Systems

Conditioned Effects Produced by Naltrexone Doses That Reduce Ethanol-Reinforced Responding in Rhesus Monkeys

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66264/1/j.1530-0277.1999.tb04173.x.pd

Review of battery electric vehicle propulsion systems incorporating flywheel energy storage

The development of battery electric vehicles (BEV) must continue since this can lead us towards a zero emission transport system. There has been an advent of the production BEVs in recent years; however their low range and high cost still remain the two important drawbacks. The battery is the element which strongly affects the cost and range of the BEV. The batteries offer either high specific power or high specific energy but not both. To provide the BEVs with the characteristic to compete with conventional vehicles it is beneficial to hybridize the energy storage combining a high energy battery with a high power source. This shields the battery from peak currents and improves its capacity and life. There are various devices which could qualify as a secondary storage system for the BEV such as high power battery, supercapacitor and high speed flywheel (FW). This paper aims to review a specific type of hybridisation of energy storage which combines batteries and high speed flywheels. The flywheel has been used as a secondary energy system in BEVs from the early 1970s when the oil crises triggered an interest in BEVs. Since the last decade the interest in flywheels has strengthened and their application in the kinetic energy recovery system (KERS) in Formula 1 has further bolstered the case for flywheels. With a number of automotive manufacturers getting involved in developing flywheels for road applications, the authors believe commercial flywheel based powertrains are likely to be seen in the near future. It is hence timely to produce a review of research and development in the area of flywheel assisted BEVs

The Role of Oligomerization and Cooperative Regulation in Protein Function: The Case of Tryptophan Synthase

The oligomerization/co-localization of protein complexes and their cooperative regulation in protein function is a key feature in many biological systems. The synergistic regulation in different subunits often enhances the functional properties of the multi-enzyme complex. The present study used molecular dynamics and Brownian dynamics simulations to study the effects of allostery, oligomerization and intermediate channeling on enhancing the protein function of tryptophan synthase (TRPS). TRPS uses a set of α/β–dimeric units to catalyze the last two steps of L-tryptophan biosynthesis, and the rate is remarkably slower in the isolated monomers. Our work shows that without their binding partner, the isolated monomers are stable and more rigid. The substrates can form fairly stable interactions with the protein in both forms when the protein reaches the final ligand–bound conformations. Our simulations also revealed that the α/β–dimeric unit stabilizes the substrate–protein conformation in the ligand binding process, which lowers the conformation transition barrier and helps the protein conformations shift from an open/inactive form to a closed/active form. Brownian dynamics simulations with a coarse-grained model illustrate how protein conformations affect substrate channeling. The results highlight the complex roles of protein oligomerization and the fine balance between rigidity and dynamics in protein function

Negation and the functional sequence

There exists a general restriction on admissible functional sequences which prevents adjacent identical heads. We investigate a particular instantiation of this restriction in the domain of negation. Empirically, it manifests itself as a restriction the stacking of multiple negative morphemes. We propose a principled account of this restriction in terms of the general ban on immediately consecutive identical heads in the functional sequence on the one hand, and the presence of a Neg feature inside negative morphemes on the other hand. The account predicts that the stacking of multiple negative morphemes should be possible provided they are separated by intervening levels of structure. We show that this prediction is borne out