Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation

A low energy optimization of the CERN-NGS neutrino beam for a theta_{13} driven neutrino oscillation search

The possibility to improve the CERN to Gran Sasso neutrino beam performances for theta_{13} searches is investigated. We show that by an appropriate optimization of the target and focusing optics of the present CNGS design, we can increase the flux of low energy neutrinos by about a factor 5 compared to the current tau optimized focalisation. With the ICARUS 2.35 kton detector at LNGS and in case of negative result, this would allow to improve the limit to sin^22 theta_{13} by an order of magnitude better than the current limit of CHOOZ at Delta m^2 approximately 3 times 10^{-3} eV^2 within 5 years of nominal CNGS running. This is by far the most sensitive setup of the currently approved long-baseline experiments and is competitive with the proposed JHF superbeam.Comment: 19 pages, 8 figure

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space

Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations one needs an algorithm which for any given $N$ and a given compact four-dimensional manifold $M$ constructs all possible triangulations of $M$ with $\leq N$ simplices. Our first result is that such algorithm does not exist. Then we discuss recursion-theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four-dimensional manifold.Comment: 8 Pages, LaTex, PUPT-132

Snapshots during the catalytic cycle of a histidine acid phytase reveal an induced fit structural mechanism

Highly engineered phytases, which sequentially hydrolyze the hexakisphosphate ester of inositol known as phytic acid, are routinely added to the feeds of monogastric animals to improve phosphate bioavailability. New phytases are sought as starting points to further optimize the rate and extent of dephosphorylation of phytate in the animal digestive tract. Multiple inositol polyphosphate phosphatases (MINPPs) are clade 2 histidine phosphatases (HP2P) able to carry out the stepwise hydrolysis of phytate. MINPPs are not restricted by a strong positional specificity making them attractive targets for development as feed enzymes. Here, we describe the characterization of a MINPP from the Gram-positive bacterium Bifidobacterium longum (BlMINPP). BlMINPP has a typical HP2P-fold but, unusually, possesses a large a-domain polypeptide insertion relative to other MINPPs. This insertion, termed the U-loop, spans the active site and contributes to substrate specificity pockets underpopulated in other HP2Ps. Mutagenesis of U-loop residues reveals its contribution to enzyme kinetics and thermostability. Moreover, four crystal structures of the protein along the catalytic cycle capture, for the first time in an HP2P, a large ligand-driven a-domain motion essential to allow substrate access to the active site. This motion recruits residues both downstream of a molecular hinge and on the U-loop to participate in specificity subsites, and mutagenesis identified a mobile lysine residue as a key determinant of positional specificity of the enzyme. Taken together, these data provide important new insights to the factors determining stability, substrate recognition, and the structural mechanism of hydrolysis in this industrially important group of enzymes

JOYCE: Jülich Observatory for cloud evolution

The Jülich Observatory for Cloud Evolution (JOYCE), located at Forschungszentrum Jülich in the most western part of Germany, is a recently established platform for cloud research. The main objective of JOYCE is to provide observations, which improve our understanding of the cloudy boundary layer in a midlatitude environment. Continuous and temporally highly resolved measurements that are specifically suited to characterize the diurnal cycle of water vapor, stability, and turbulence in the lower troposphere are performed with a special focus on atmosphere–surface interaction. In addition, instruments are set up to measure the micro- and macrophysical properties of clouds in detail and how they interact with different boundary layer processes and the large-scale synoptic situation. For this, JOYCE is equipped with an array of state-of-the-art active and passive remote sensing and in situ instruments, which are briefly described in this scientific overview. As an example, a 24-h time series of the evolution of a typical cumulus cloud-topped boundary layer is analyzed with respect to stability, turbulence, and cloud properties. Additionally, we present longer-term statistics, which can be used to elucidate the diurnal cycle of water vapor, drizzle formation through autoconversion, and warm versus cold rain precipitation formation. Both case studies and long-term observations are important for improving the representation of clouds in climate and numerical weather prediction models

Neutrino oscillation physics at an upgraded CNGS with large next generation liquid Argon TPC detectors

The determination of the missing $U_{e3}$ element (magnitude and phase) of the PMNS neutrino mixing matrix is possible via the detection of \numu\to\nue oscillations at a baseline $L$ and energy $E$ given by the atmospheric observations, corresponding to a mass squared difference $E/L \sim \Delta m^2\simeq 2.5\times 10^{-3} eV^2$. While the current optimization of the CNGS beam provides limited sensitivity to this reaction, we discuss in this document the physics potential of an intensity upgraded and energy re-optimized CNGS neutrino beam coupled to an off-axis detector. We show that improvements in sensitivity to $\theta_{13}$ compared to that of T2K and NoVA are possible with a next generation large liquid Argon TPC detector located at an off-axis position (position rather distant from LNGS, possibly at shallow depth). We also address the possibility to discover CP-violation and disentangle the mass hierarchy via matter effects. The considered intensity enhancement of the CERN SPS has strong synergies with the upgrade/replacement of the elements of its injector chain (Linac, PSB, PS) and the refurbishing of its own elements, envisioned for an optimal and/or upgraded LHC luminosity programme.Comment: 37 pages, 20 figure