Suppression of viscous fluid fingering: a piecewise constant-injection process

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this letter we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.Comment: Published in Phys. Rev.

Gravity-driven instability in a spherical Hele-Shaw cell

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review

On Bargmann Representations of Wigner Function

By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of Wigner function (W). A non-integral representation is presented in terms of a quadratic form V*FV, where F is a self-adjoint matrix whose entries are tabulated functions and V is a vector depending in a simple recursive way on the derivatives of the Bargmann function. Such a representation may be of use in numerical computations. We discuss a relation involving the geometry of Wigner function and the spacial uncertainty of the coherent state basis we use to represent it.Comment: accepted for publication in J. Phys. A: Math. and Theo

A goal programming methodology for multiobjective optimization of distributed energy hubs operation

This paper addresses the problem of optimal energy flow management in multicarrier energy networks in the presence of interconnected energy hubs. The overall problem is here formalized by a nonlinear constrained multiobjective optimization problem and solved by a goal attainment based methodology. The application of this solution approach allows the analyst to identify the optimal operation state of the distributed energy hubs which ensures an effective and reliable operation of the multicarrier energy network in spite of large variations of load demands and energy prices. Simulation results obtained on the 30 bus IEEE test network are presented and discussed in order to demonstrate the significance and the validity of the proposed method

Semiclassical Propagation of Wavepackets with Real and Complex Trajectories

We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller's thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.Comment: revised text, 24 pages, 6 figure

Affine arithmetic-based methodology for energy hub operation-scheduling in the presence of data uncertainty

In this study, the role of self-validated computing for solving the energy hub-scheduling problem in the presence of multiple and heterogeneous sources of data uncertainties is explored and a new solution paradigm based on affine arithmetic is conceptualised. The benefits deriving from the application of this methodology are analysed in details, and several numerical results are presented and discussed

Geodesics around line defects in elastic solids

Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This way, the deformation field is described by non-Euclidean metric that incorporates the boundary imposed by the defects. A possible way of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work, we find the exact solution for the geodesic equation for elastic medium with a generic line defect, the dispiration, that can either be a screw dislocation or a wedge disclination for particular choices of its parameters.Comment: 10 pages, Latex, 4 figures, accepted for publication in Phys. Lett.

Gravity-driven instability in a spherical Hele-Shaw cell

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review

A conjugate for the Bargmann representation

In the Bargmann representation of quantum mechanics, physical states are mapped into entire functions of a complex variable z*, whereas the creation and annihilation operators $\hat{a}^\dagger$ and $\hat{a}$ play the role of multiplication and differentiation with respect to z*, respectively. In this paper we propose an alternative representation of quantum states, conjugate to the Bargmann representation, where the roles of $\hat{a}^\dagger$ and $\hat{a}$ are reversed, much like the roles of the position and momentum operators in their respective representations. We derive expressions for the inner product that maintain the usual notion of distance between states in the Hilbert space. Applications to simple systems and to the calculation of semiclassical propagators are presented.Comment: 15 page