Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Total energy shaping of a class of underactuated Port-Hamiltonian Systems using a new set of closed-loop potential shape variables

This paper proposes a method for designing set-point regulation controllers for a class of underactuated mechanical systems in Port-Hamiltonian System (PHS) form. A new set of potential shape variables in closed loop is proposed, which can replace the set of open loop shape variables-the configuration variables that appear in the kinetic energy. With this choice, the closed-loop potential energy contains free functions of the new variables. By expressing the regulation objective in terms of these new potential shape variables, the desired equilibrium can be assigned and there is freedom to reshape the potential energy to achieve performance whilst maintaining the PHS form in closed loop. This complements contemporary results in the literature, which preserve the open-loop shape variables. As a case study, we consider a robotic manipulator mounted on a flexible base and compensate for the motion of the base while positioning the end effector with respect to the ground reference. We compare the proposed control strategy with special cases that correspond to other energy shaping strategies previously proposed in the literature.

A New Class Of Photo-Cross-Linkable Side-Chain Liquid Crystalline Polymers Containing Bis(Benzylidene)Cyclohexanone Units

This paper reports a new class of photo-cross-linkable side chain liquid crystalline polymers (PSCLCPs) based on the bis(benzylidene)cyclohexanone unit, which functions as both a mesogen and a photoactive center. Polymers with the bis(benzylidene)cyclohexanone unit and varying spacer length have been synthesized. Copolymers of bis(benzylidene)cyclohexanone containing monomer and cholesterol benzoate containing monomer with different compositions have also been prepared. All these polymers have been structurally characterized by spectroscopic techniques. Thermal transitions were studied by DSC, and mesophases were identified by polarized light optical microscopy (POM). The intermediate compounds OH-x, the monomers SCLCM-x, and the corresponding polymers PSCLCP-x, which are essentially based on bis(benzylidene)cyclohexanone, all show a nematic mesophase. Transition temperatures were observed to decrease with increasing spacer length. The copolymers with varying compositions exhibit a cholesteric mesophase, and the transition temperatures increase with the cholesteric benzoate units in the copolymer. Photolysis of the low molecular weight liquid crystalline bis(benzylidene)-cyclohexanone compound reveals that there are two kinds of photoreactions in these systems: the EZ photoisomerization and 2 pi + 2 pi addition. The EZ photoisomerization in the LC phase disrupts the parallel stacking of the mesogens, resulting in the transition from the LC phase to the isotropic phase. The photoreaction involving the 2 pi + 2 pi addition of the bis(benzylidene)cyclohexanone units in the polymer results in the cross-linking of the chains. The liquid crystalline induced circular dichroism (LCICD) studies of the cholesterol benzoate copolymers revealed that the cholesteric supramolecular order remains even after the photo-cross-linking.

Novel Functionalised Troger's Bases: Synthesis of a New Class of Troger's Base Analogues Containing Dicarboxyl Functionality

The synthesis of three new Troger's base analogues, each functionalized with two carboxyl groups, is described. Copyright.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the orthogonal and the nonorthogonal amplify-and-forward (NAF) protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Moreover our code construction for the OAF protocol incurs less delay. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. The variable-NSDF protocol is shown to improve on the DMT of the best previously known static protocol when the number of relays is greater than two. Also included is a DMT optimal code construction for the NAF protocol.

Universality class of the reversible-irreversible transition in sheared suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behavior as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved directed percolation models. This leads to predictions for the scaling behavior of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.

Portrait of the dancing school class of Therese Molling (second row third from right); Germany.

Mille Ottling ran the dancing school. Therese Molling's daughter Liesel (Elizabeth) Gottschalk and brother Hal attended the same school during the mid 1920s

Graduation portrait including Otto Gersuny, class of 1908, K. & K. Gymnasium; Teplitz, Germany (Teplice, Czech Republic).

Otto Gersuny (1890-1964), third row from the front wearing cap (see arrow)