波城的大学

We establish upper bounds for the weak and strong error resulting from a perturbation of the noise driving the stochastic Burgers equation, where we assume the noise to be additive and of trace class and the initial value to be sufficiently regular. More specifically, let Qi, i∈{1,2}, be positive trace class operators on L2(0,1) and for i∈{1,2} let Xi:[0,T]×[0,1]×Ω→R be the solution to the stochastic Burgers equation driven by a Qi-Brownian motion WQi:[0,T]×Ω→L2(0,1) on the temporal-spatial domain [0,T]×[0,1]. We prove a weak error bound of the form|E[φ(X1(T,⋅))]−E[φ(X2(T,⋅))]|≲‖(−A)−1−(Q1−Q2)‖L1(L2), where φ:L2(0,1)→R is a sufficiently smooth function, ‖⋅‖L1(L2) is the trace class norm for operators on L2(0,1), and A:D(A)⊆L2(0,1)→L2(0,1) is the one-dimensional Dirichlet Laplacian that represents the leading term in the Burgers equation. In addition, we prove a strong error bound of the formE∫01|X1(T,z)−X2(T,z)|2dz≲‖(−A)−12−|Q112−Q212|‖L2(L2)2, where ‖⋅‖L2(L2) is the Hilbert–Schmidt norm for operators on L2(0,1). In particular, our results provide upper bounds for the weak and strong error arising when approximating the trace class noise by finite-dimensional noise; the rates we obtain reflect the general philosophy that the weak convergence rate should be twice the strong rate.

In this paper, a new method for three-phase equilibrium calculations at constant pressure and enthalpy (PH flash) is presented. Michelsen’s Q-function is derived from the Lagrangian of the constrained maximization of entropy with respect to mole numbers and temperature, subject to the enthalpy balance constraint. This saddle point problem is transformed into an unconstrained minimization one by using an augmented Q-function. The proposed hybrid algorithm consists of Newton iterations (with line search to ensure a decrease of the objective function) combined with a trust-region method when the Hessian matrix is not positive definite (that is, the Newton method fails to provide a descent direction). A small number of partial-Newton iterations (in which some partial derivatives are neglected in the Hessian) are performed in the early iteration stages. Based on Michelsen’s foundational work, we detail for the first time the implementation and results of the application of the corresponding hybrid algorithm to solve two- and three-phase isenthalpic flash problems by minimization of the augmented Q-function with respect to mole numbers and temperature, including analytical expressions of all required partial derivatives. We conduct extensive convergence tests within the P-H plane, using several representative fluids, including examples showing narrow-boiling behavior. The proposed calculation algorithm turns out to be robust and efficient. Convergence behavior is analyzed in detail for several selected conditions, including very difficult points. Convergence is obtained for the quasi-totality of test points; some outliers require the use of the extremely robust, but slower nested approach. The results demonstrate that the proposed hybrid algorithm is a strong candidate for robust and fast isenthalpic flash routines in complex compositional simulations (as for CO2 storage applications), considering two- and three-phase equilibria and including a narrow-boiling behavior.

Yersinopine, a nicotianamine-like metallophore, was recently identified through biochemical analyses, but its in vivo production and functional role remain uncharacterized. In Yersinia pseudotuberculosis and its recent descendant Yersinia pestis, the cnt operon (cntPQRLMI) putatively encodes the biosynthesis and transport of yersinopine. In Y. pestis, however, two frameshift mutations disrupt cntQ, which encodes the predicted permease for yersinopine-metal complexes. This pseudogenization raises critical questions about the functional relevance of yersinopine in these closely related species. Here, we show that cnt operon expression is repressed by the zinc uptake regulator Zur and that both Y. pestis and Y. pseudotuberculosis secrete yersinopine under zinc-limited conditions. Unexpectedly, the operon mediates iron uptake in Y. pseudotuberculosis but supports zinc acquisition in Y. pestis. Moreover, targeted disruption of cntQ in Y. pseudotuberculosis shifts metal specificity from iron to zinc, mimicking the Y. pestis phenotype. Collectively, our results suggest that a single pseudogenization event could rewire metal uptake specificity. Our findings illustrate how evolutionary genome reduction can reshape bacterial physiology.

Non-destructive techniques such as the contact sponge method (CSM) and the Karsten tube have been developed to assess the water absorption properties of building materials during field measurements. In contrast, laboratory investigations typically rely on capillary rise tests (CR) on centimetric specimens imposing a one-dimensional water flow. Although the results obtained from these methods are qualitatively comparable, a robust quantitative correlation is still lacking. An analytical expression has previously been proposed to estimate the sorptivity from measurements with non-destructive techniques, based on the assumption that the water penetration depth equals the lateral spreading of water on the material surface. In this study, we investigate the water absorption processes induced by the contact sponge method, by combining neutron radiography, which allows direct visualization of water penetration, with conventional capillary rise tests based on gravimetric measurements. Sandstones and limestones with porosities ranging from 10

We develop, simulate and extend an initial proposition by Chaves et al. (J. Stat. Phys., vol. 113, no. 5-6, 2003, pp. 643-692) concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this paper we focus on the important underlying Gaussian framework. Presently, the statistical spatial structure of this velocity field is consistent with a divergence-free fractional Gaussian vector field that encodes all known properties of homogeneous and isotropic fluid turbulence at a given finite Reynolds number, up to second-order statistics. The temporal structure of the velocity field is introduced through a stochastic evolution of the respective Fourier modes. In the simplest picture, Fourier modes evolve according to an Ornstein-Uhlenbeck process, where the characteristic time scale depends on the wave-vector amplitude. For consistency with direct numerical simulations (DNS) of the Navier-Stokes equations, this time scale is inversely proportional to the wave-vector amplitude. As a consequence, the characteristic velocity that governs the eddies is independent of their size and is related to the velocity standard deviation, which is consistent with some features of the so-called sweeping effect. To ensure differentiability in time while respecting the Markovian nature of the evolution, we use the methodology developed by Viggiano et al. (J. Fluid Mech., vol. 900, 2020, A27) to propose a fully consistent stochastic picture. We finally derive analytically all statistical quantities in a continuous set-up and develop precise and efficient numerical schemes of the corresponding periodic framework. Both exact predictions and numerical estimations of the model are compared with DNS provided by the Johns Hopkins database.