On the singularity formation and relaxation to equilibrium in 1D Fokker–Planck model with superlinear drift

We consider a class of Fokker–Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite critical mass above which the measure minimising the associated entropy functional displays a singular component. Our approach, which addresses the one-dimensional case, is based on a reformulation of the problem in terms of the pseudo-inverse distribution function. Motivated by the structure of the equation in the new variables, we establish a general framework for global-in-time existence, uniqueness and regularity of monotonic viscosity solutions to a class of nonlinear degenerate (resp. singular) parabolic equations, using as a key tool comparison principles and maximum arguments. We then focus on a specific equation and study in more detail the regularity and dynamics of solutions. In particular, blow-up behaviour, formation of condensates (i.e. Dirac measures at zero) and long-time asymptotics are investigated. As a consequence, in the mass-supercritical case, solutions will blow up in L∞ in finite time and—understood in a generalised, measure sense—they will eventually have condensate. We further show that the singular part of the measure solution does in general interact with the density and that condensates can be transient. The equations considered are motivated by a model for bosons introduced by Kaniadakis and Quarati (1994), which has a similar entropy structure and a critical mass if d ≥ 3

Quantum Numbers for Excitations of Bose-Einstein Condensates in 1D Optical Lattices

The excitation spectrum and the band structure of a Bose-Einstein condensate in a periodic potential are investigated. Analyses within full 3D systems, finite 1D systems, and ideal periodic 1D systems are compared. We find two branches of excitations in the spectra of the finite 1D model. The band structures for the first and (part of) the second band are compared between a finite 1D and the fully periodic 1D systems, utilizing a new definition of a effective wavenumber and a phase-slip number. The upper and lower edges of the first gap coincide well between the two cases. The remaining difference is explained by the existence of the two branches due to the finite-size effect.Comment: 5 pages, 9 figure

Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approximation it provides a rich mixed phase space dynamics with regular and chaotic regions. By increasing the kick-strength a bifurcation leads to the appearance of self-trapping states localized on regular islands. This self-trapping is also found for the many particle system, however in general suppressed by coherent many particle tunneling oscillations. The tunneling time can be calculated from the quasi-energy splitting of the corresponding Floquet states. By varying the kick-strength these quasi-energy levels undergo both avoided and even actual crossings. Therefore stimulation or complete destruction of tunneling can be observed for this many particle system

New primers for promising single-copy genes in fungal phylogenetics and systematics

Developing powerful phylogenetic markers is a key concern in fungal phylogenetics. Here we report degenerate primers that amplify the single-copy genes Mcm7 (MS456) and Tsr1 (MS277) across a wide range of Pezizomycotina (Ascomycota). Phylogenetic analyses of 59 taxa belonging to the Eurotiomycetes, Lecanoromycetes, Leotiomycetes, Lichinomycetes and Sordariomycetes, indicate the utility of these loci for fungal phylogenetics at taxonomic levels ranging from genus to class. We also tested the new primers in silico using sequences of Saccharomycotina, Taphrinomycotina and Basidiomycota to predict their potential of amplifying widely across the Fungi. The analyses suggest that the new primers will need no, or only minor sequence modifications to amplify Saccharomycotina, Taphrinomycotina and Basidiomycota

Critical periods of increased fetal vulnerability to a maternal high fat diet

Background: Fetal adaptations to high fat (HF) diet in utero (IU) that may predispose to Metabolic Syndrome (MetS) in adulthood include changes in fetal hepatic gene expression. Studies were performed to determine whether maternal exposure to HF diet at different stages during pregnancy had different effects on the fetus, including hepatic gene expression. Methods: Female wild type mice were fed either a HF or breeding chow (C) for 2 wks prior to mating. The experimental groups were composed of embryonic day (e) 18.5 fetuses obtained from WT female mice that were fed HF (HF, 35.5% fat) or breeding chow (C, 9.5% fat) for 2 wk before mating until e9.5 of pregnancy (periconception-midpregnancy). At e9.5 dams were switched to the opposite diet (C-HF or HF-C). Results: Exposure to HF diet throughout pregnancy reduced maternal weight gain compared to C diet (p \u3c 0.02 HF vs. C). HF-C dams had significantly decreased adiponectin levels and litter size when compared to C-HF (p \u3c 0.02 HF-C vs C-HF). Independent of the timing of exposure to HF, fetal weight and length were significantly decreased when compared to C diet (HF, C-HF and HF-C vs. C p \u3c 0.02). HF diet during the second half of pregnancy increased expression of genes in the fetal liver associated with fetal growth (C-HF vs C p \u3c 0.001), glucose production (C-HF vs C p \u3c 0.04), oxidative stress and inflammation (C-HF vs C p \u3c 0.01) compared to C diet. Conclusions: This model defines that there are critical periods during gestation in which the fetus is actively shaped by the environment. Early exposure to a HF diet determines litter size while exposure to HF during the second half of pregnancy leads to dysregulation of expression of key genes responsible for fetal growth, hepatic glucose production and oxidative stress. These findings underscore the importance of future studies designed to clarify how these critical periods may influence future risk of developing MetS later in life

Reconstruction and flux-balance analysis of the Plasmodium falciparum metabolic network

In the paper we present a metabolic reconstruction and flux-balance analysis (FBA) of Plasmodium falciparum, the primary agent of malaria. The compartmentalized metabolic network of the parasite accounts for 1001 reactions and 616 metabolites. Enzyme–gene associations were established for 366 genes and 75% of all enzymatic reactions.The model was able to reproduce phenotypes of experimental gene knockout and drug inhibition assays with up to 90% accuracy. The model also can be used to efficiently integrate mRNA-expression data to improve the accuracy of metabolic predictions.Using FBA of the reconstructed metabolic network, we identified 40 enzymatic drug targets (i.e. in silico essential genes) with no or very low sequence identity to human proteins.We experimentally tested one of the identified drug targets, nicotinate mononucleotide adenylyltransferase, using a recently discovered small-molecule inhibitor

Elevated levels of diesel range organic compounds in groundwater near Marcellus gas operations are derived from surface activities

Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences of the United States of American 112 (2015): 13184-13189, doi: 10.1073/pnas.1511474112 .Hundreds of organic chemicals are utilized during natural gas extraction via high volume hydraulic fracturing (HVHF). However, it is unclear if these chemicals, injected into deep shale horizons, reach shallow groundwater aquifers and impact local water quality, either from deep underground injection sites or from the surface or shallow subsurface. Here, we report detectable levels of organic compounds in shallow groundwater samples from private residential wells overlying the Marcellus Shale in northeastern Pennsylvania. Analyses of purgeable and extractable organic compounds from 64 groundwater samples revealed trace levels of volatile organic compounds, well below the Environmental Protection Agency’s maximum contaminant levels, and low levels of both gasoline range (GRO; 0-8 ppb) and diesel range organic compounds (DRO; 0-157 ppb). A compound-specific analysis revealed the presence of bis(2-ethylhexyl)phthalate, which is a disclosed HVHF additive, that was notably absent in a representative geogenic water sample and field blanks. Pairing these analyses with 1) inorganic chemical fingerprinting of deep saline groundwater, 2) characteristic noble gas isotopes, and 3) spatial relationships between active shale gas extraction wells and wells with disclosed environmental health and safety (EHS) violations, we differentiate between a chemical signature associated with naturally occurring saline groundwater and a one associated with alternative anthropogenic routes from the surface (e.g., accidental spills or leaks). The data support a transport mechanism of DRO to groundwater via accidental release of fracturing fluid chemicals derived from the surface rather than subsurface flow of these fluids from the underlying shale formation.The authors thank Duke University’s Pratt School of Engineering and the National Science Foundation’s CBET Grant Number 1336702 and NSF EAGER (EAR-1249255) for financial support.2016-04-1

The AFLOW Fleet for Materials Discovery

The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first principles calculations, and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational modules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermo-mechanical properties and more. The AFLOW data repository is publicly accessible online at aflow.org, with more than 1.7 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available.Comment: 14 pages, 8 figure

Ionization via Chaos Assisted Tunneling

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity via chaotic diffusion. The specific system is realistic : it is the hydrogen atom exposed to either linearly or circularly polarized microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar statistical fluctuation properties of the energy and the ionization rate, especially to enhanced fluctuations compared to the purely chaotic case. An appropriate random matrix model, whose predictions are analytically derived, describes accurately these statistical properties.Comment: 30 pages, 11 figures, RevTeX and postscript, Physical Review E in pres