Linear drainage in a fresh groundwater fringe above saline groundwater

Possible flow variants as a function of the determining physical parameters are analyzed within the framework of the boundary-value problem of horizontal slit drainage in a fresh groundwater fringe above saline groundwater. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 64–77, November–December, 2006.     

Numerical Investigation of Multi-Jet Channel Flows

The results of a numerical simulation of the three-dimensional outflow of a system of circular supersonic turbulent jets into a cocurrent supersonic (or subsonic) air flow in a partially bounded region are given. Solutions are obtained by the splitting method using a matrix sweep of the parabolized Navier-Stokes equations. Assuming that the flow is nonseparated in the boundary layer, features of the three-dimensional structure of the jet system are investigated as functions of the pressure ratio number and the jet and cocurrent flow Mach numbers.     

Phonon-assisted zero bias anomaly in a single-molecule quantum dot coupled to the Luttinger liquid leads

The joint effects of the electron–phonon interaction and electron–electron interaction in the Luttinger liquid leads on nonequilibrium transport through a single-molecule transistor in the Kondo regime are investigated by using the improved canonical transformation scheme and equation of motion approach. For weak intralead electron interaction, a pronounced dip around zero bias, accompanied by a series of discrete single-electron tunneling peaks is observed in the differential conductance. With the increase of the intralead interaction, the phonon-assisted peaks turn into dips, which demonstrates a phonon-assisted two-channel Kondo physics. For a certain region of interaction strength the inelastic electron tunneling can dominate electron transport. Our results well explain the experiments of zero bias anomaly.     

Numerical analysis for transverse microbead trapping using 30 MHz focused ultrasound in ray acoustics regime

We have recently devised a remote acoustic manipulation method with high frequency focused ultrasonic beam of 30–200 MHz, and experimentally realized it by the intensity gradient near the beam’s focus. A two-dimensional (or transverse) acoustic trapping was demonstrated by directly applying the acoustic radiation force on lipid spheres and leukemia cells that were individually moved towards the focus. Only longitudinal waves were then considered because both target and propagation media involved were fluid e.g., water or phosphate buffer saline.     

状态转移下的利率预期与误差学习假说

采用线性回归和状态转移模型讨论利率预期的"误差学习假说"和不同期限利率预测误差之间的关联性,并考虑带有风险溢价时预测误差的作用.分析发现,1年期限的"误差学习假说"在银行间国债市场中是成立的,不同期限的利率预期对预测误差的反应呈现一定的独立性,不同的状态中预测误差和风险溢价对利率预期的影响是不同的,考虑风险溢价有助于提升对利率预期变动的解释.     

Analysis of combustion regimes and conditional statistics of autoigniting turbulent n-heptane sprays

DNS is performed for a statistically one dimensional layer of a spray region resembling diesel engine conditions. The group and collective combustion regimes are identified according to the ratio of the chemical and transport time scales for a single droplet. The statistics in group combustion are similar with those in gas phase combustion. The collective combustion regime involves interspersed rich regions with different dissipation characteristics. Reasonable agreements are shown with the scaled AMC model and the linear evaporation model in the ranges of meaningful probability. Initially the evaporation terms are dominant in the budgets of the conditional enthalpy equation. After ignition the chemical reaction term becomes dominant to be balanced by the time rate of change term. For modeling turbulent spray combustion it may not be essential to consider detailed micro structures around each droplet, unless in the droplet combustion regime.     

Crystal Memory near Discontinuous Triacylglycerol Phase Transitions: Models,Metastable Regimes,and Critical Points

It is proposed that “crystal memory”, observed in a discontinuous solid-liquid phase transition of saturated triacylglycerol (TAG) molecules, is due to the coexistence of solid TAG crystalline phases and a liquid TAG phase, in a superheated metastable regime. Such a coexistence has been detected. Solid crystals can act as heterogeneous nuclei onto which molecules can condense as the temperature is lowered. We outlined a mathematical model, with a single phase transition, that shows how the time-temperature observations can be explained, makes predictions, and relates them to recent experimental data. A modified Vogel-Fulcher-Tammann (VFT) equation is used to predict time-temperature relations for the observation of “crystal memory” and to show boundaries beyond which “crystal memory” is not observed. A plot of the lifetime of a metastable state versus temperature, using the modified VFT equation, agrees with recent time-temperature data. The model can be falsified through its predictions: the model possesses a critical point and we outline a procedure describing how it could be observed by changing the hydrocarbon chain length. We make predictions about how thermodynamic functions will change as the critical point is reached and as the system enters a crossover regime. The model predicts that the phenomenon of “crystal memory” will not be observed unless the system is cooled from a superheated metastable regime associated with a discontinuous phase transition.     

Identification of flow regimes and determination of the boundaries for magnetized fluidized bed with Geldart-B particles

The magnetized fluidized bed (MFB) with Geldart-B particles exhibits many distinct flow regimes depending on the magnetic field intensity (H) and gas velocity (U_g). The identification of these regimes was reviewed for the MFB with magnetizable particles and that with binary admixture of magnetizable and nonmagnetizable particles. Meanwhile, methods for determining the boundaries between two adjacent flow regimes were clarified. The MFB state was found to depend not only on H and U_g but also on their application sequence (i.e., operation mode) within certain operating zones. The dependence feature arose from that the MFB therein could have different equilibrium states for the same combination of H and U_g. Furthermore, such a polymorphic characteristic of the MFB was revealed to result from the internal friction among the particles that were in unfluidized/packed state. Many of the MFB states were demonstrated to be in metastable equilibrium. Nevertheless, they differed significantly from the metastates well-known in the discipline of physical chemistry, such as supercooling and superheated. In fact, they belonged to the amorphous/glass state. This review will deepen our hydrodynamic understanding of the MFB and further promote its commercial application in the chemical and biochemical industries.     

An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

In this paper, an implicit‐explicit two‐step backward differentiation formula (IMEX‐BDF2) together with finite difference compact scheme is developed for the numerical pricing of European and American options whose asset price dynamics follow the regime‐switching jump‐diffusion process. It is shown that IMEX‐BDF2 method for solving this system of coupled partial integro‐differential equations is stable with the second‐order accuracy in time. On the basis of IMEX‐BDF2 time semi‐discrete method, we derive a fourth‐order compact (FOC) finite difference scheme for spatial discretization. Since the payoff function of the option at the strike price is not differentiable, the results show only second‐order accuracy in space. To remedy this, a local mesh refinement strategy is used near the strike price so that the accuracy achieves fourth order. Numerical results illustrate the effectiveness of the proposed method for European and American options under regime‐switching jump‐diffusion models.     

Attractors and Long Time Behavior of von Karman Thermoelastic Plates

This paper undertakes a study of asymptotic behavior of solutions corresponding to von Karman thermoelastic plates. A distinct feature of the work is that the model considered has no added dissipation—particularly mechanical dissipation typically added to plate equation when long time-behavior is considered. Thus, the model consists of undamped oscillatory plate equation strongly coupled with heat equation. Nevertheless we are able to show that the ultimate (asymptotic) behavior of the von Karman evolution is described by finite dimensional global attractor. In addition, the obtained estimate for the dimension and the size of the attractor are independent of the rotational inertia parameter γ and heat/thermal capacity κ, where the former is known to change the character of dynamics from hyperbolic (γ>0) to parabolic like (γ=0). Other properties of attractors such as additional smoothness and upper-semicontinuity with respect to parameters γ and κ are also established. The main ingredients of the proofs are (i) sharp regularity of Airy’s stress function, and (ii) newly developed (Chueshov and Lasiecka in Memoirs of AMS, in press) “compensated” compactness methods applicable to non-compact dynamics. I. Lasiecka’s research partially supported by the NSF Grant DMS-0104305 and ARO Grant DAAD19-02-10179.