Biocatalytic Feedback‐Controlled Non‐Newtonian Fluids

Non‐Newtonian fluids are ubiquitous in daily life and industrial applications. Herein, we report an intelligent fluidic system integrating two distinct non‐Newtonian rheological properties mediated by an autocatalytic enzyme reaction. Associative polyelectrolytes bearing a small amount of ionic and alkyl groups are engineered: by carefully balancing the charge density and the hydrophobic effect, the polymer solutions demonstrate a unique shear thickening property at low pH while shear thinning at high pH. The urea‐urease clock reaction is utilized to program a feedback‐induced pH change, leading to a strong upturn of the nonlinear viscoelastic properties. As long as the chemical fuel is supplied, two distinct non‐Newtonian states can be achieved with a tunable lifetime span. As a proof of concept, we demonstrate how the physical energy‐driven nonequilibrium properties can be manipulated by a chemical‐fueled process.     

Time‐resolved in situ tomography for the analysis of evolving metal‐foam granulates

An experimental setup has been developed that allows for capturing up to 25 tomograms s^?1 using the white X‐ray beam at the experimental station EDDI of BESSY II, Berlin, Germany. The key points are the use of a newly developed, precise and fast rotation stage, a very efficient scintillator and a fast CMOS camera. As a first application, the foaming of aluminium alloy granules at 923 K was investigated in situ. Formation and growth of bubbles in the liquid material were observed and found to be influenced by the limited thermal conductivity in the bulk granules. Changes that took place between two tomographic frames separated in time by 39 ms could be detected and analysed quantitatively.     

Above-threshold ionization photoelectron spectrum from quantum trajectory

Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical and experimental results. Comparing BM with the classical trajectory Monte-Carlo method, we conclude that quantum potential may play a key role to reproduce the spectrum of ATI. Our work may present a new approach to understanding quantum phenomena in intense laser-atom physics with the image of trajectory.     

Bayesian Nonparametric Estimation for Reinforced Markov Renewal Processes

Starting from the definitions and the properties of reinforced renewal processes and reinforced Markov renewal processes, we characterize, via exchangeability and de Finetti’s representation theorem, a prior that consists of a family of Dirichlet distributions on the space of Markov transition matrices and beta-Stacy processes on distribution functions. Then, we show that this family is conjugate and give some estimate results.

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Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

A prediction problem in

For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .

     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Stochastic resonance in a model of opinion formation on small-world networks

We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a “fashion wave”. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed. Received 19 December 2001     

Ultrafast dynamics in the excited hydrogen atom transfer states of ammonia clusters

Neutral ammonia clusters (NH₃)_m are photo-excited to the electronic state by a deep UV femtosecond laser pump pulse. Within a few hundred femtoseconds a significant fraction of the clusters rearrange to form an H-transfer state (NH₃)_m-2NH₄(3s)NH₂ with the subunit NH₄ in its 3s electronic ground state. This state is then electronically excited by a time-delayed infrared control pulse of variable wavelength. Finally, a third (probe) pulse in the UV ionizes the clusters for detection. The lifetime of the excited (NH₃)_m-2NH₄(3p)NH₂ states is found to vary between 2.7 and 0.13 ps depending on cluster size and excitation energy. It increases drastically upon deuteration. The corresponding cluster size-dependent photoelectron spectra allow us to disentangle the underlying energetics of the excitation and ionization process and reveal additional processes, such as nonresonant ionization or dissociative ionization. The experimental findings suggest that the excited H-transfer ammonia complexes with m > 2 are deactivated by an internal conversion process back to the electronically lowest H-transfer state followed by fast dissociation. Received 22 September 2001 and Received in final form 31 January 2002     

On the Continuity of Pathwise Solutions to Langevin Equations in Infinite Dimensions

We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d _t =db _t +T( _t )dt with the initial data ₀=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C _B consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d _t =