Search results for "fluids"
showing 10 items of 1936 documents
New Theoretical Solution of Stage-Discharge Relationship for Slit Weirs
2018
In this paper, the flow-process of a slit weir was analyzed on the basis of a theorem of dimensional analysis and incomplete selfsimilarity theory. The theoretically deduced stage-discharge formula then was calibrated using experimental data obtained for a ratio between the weir and the channel width, ranging from 0.05 to 0.25. The deduced stage-discharge relationship allowed measuring discharge values characterized by errors that, for 98% of the measured values, were less than or equal to 5%. The performance of the proposed theoreticalstage-discharge formula also was improved by introducing the Reynolds number (for 98.5% of the measured values the error was less than or equal to 5%, and th…
Resonance between Cantor sets
2007
Let $C_a$ be the central Cantor set obtained by removing a central interval of length $1-2a$ from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if $\log b/\log a$ is irrational, then \[ \dim(C_a+C_b) = \min(\dim(C_a) + \dim(C_b),1), \] where $\dim$ is Hausdorff dimension. More generally, given two self-similar sets $K,K'$ in $\RR$ and a scaling parameter $s>0$, if the dimension of the arithmetic sum $K+sK'$ is strictly smaller than $\dim(K)+\dim(K') \le 1$ (``geometric resonance''), then there exists $r<1$ such that all contraction ratios of the similitudes defining $K$ and $K'$ are powers of $r$ (``algebraic resonance…
Lackadaisical Quantum Walks with Multiple Marked Vertices
2019
The concept of lackadaisical quantum walk – quantum walk with self loops – was first introduced for discrete-time quantum walk on one-dimensional line [8]. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid [16].
Nonlinear embeddings: Applications to analysis, fractals and polynomial root finding
2016
We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors, coefficients of a generating function...) to their ordinary sum at $\kappa \to \infty$. We show that $\mathcal{B}_{\kappa}$-embeddings can be used to design nonlinear irreversible processes through this connection. A number of examples of increasing complexity are worked out to illustrate the possibilities uncovered by this concept. These include not only smooth functions but also fractals on the real line and on the complex plane. As an application, we use $\mat…
Exceptional Quantum Walk Search on the Cycle
2016
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips, staying in a uniform probability distribution for all time. We prove that the one-dimensional periodic lattice or cycle with any arrangement of marked vertices is such an exceptional configuration. Using this discovery, we construct a search problem where the quantum walk's random sampling yields an arbitrary speedup in query complexity over the classical random walk's hitting time. In this context, however, the mixing time to prepare the initial uniform state…
Nonmalleable encryption of quantum information
2008
We introduce the notion of "non-malleability" of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a "unitary 2-design" [Dankert et al.], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of (d^2-1)^2+1 on the number of unitaries in a 2-design [Gross et al.], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with =…
Adjacent Vertices Can Be Hard to Find by Quantum Walks
2017
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show that if the search space contains more than one marked element, their placement may drastically affect the performance of the search. More specifically, we study search by quantum walks on general graphs and show a wide class of configurations of marked vertices, for which search by quantum walk needs \(\varOmega (N)\) steps, that is, it has no speed-up over the classical exhaustive search. The demonstrated configurations occur for certain placements of …
A coupled Finite Volume–Smoothed Particle Hydrodynamics method for incompressible flows
2016
Abstract An hybrid approach is proposed which allows to combine Finite Volume Method (FVM) and Smoothed Particle Hydrodynamics (SPH). The method is based on the partitioning of the computational domain into a portion discretized with a structured grid of hexahedral elements (the FVM-domain ) and a portion filled with Lagrangian particles (the SPH-domain ), separated by an interface made of triangular elements. A smooth transition between the solutions in the FVM and SPH regions is guaranteed by the introduction of a layer of grid cells in the SPH-domain and of a band of virtual particles in the FVM one (both neighboring the interface), on which the hydrodynamic variables are obtained throug…
Damping effect on the ITER vacuum vessel displacements during slow downward locked and rotating asymmetric vertical displacement events
2018
Abstract In this paper, we present the electromechanical coupled analysis of the ITER vacuum vessel in case of slow downward locked and rotating Asymmetric VDEs. The numerical model for simulating the AVDE includes the asymmetric distribution of the halo currents obtained by a suitable 3D kink perturbation of a slow VDE downward computed by the 2D code DINA. In the case of a rotational AVDE, the rotation frequency of the kink asymmetry has been chosen to be ω = 2π × 5 rad/s. The model includes the mesh of the main passive components facing the plasma. The whole torus (360 degrees) has been discretized. It is shown that the very high complexity of the numerical model can be suitably treated.…
Polymerization of methyl methacrylate through ionizing radiation in CO2-based dense systems
2000
Herein, we report the use of ionizing radiation to induce a dispersion polymerization reaction in dense CO2. As a model system, the polymerization of methyl methacrylate in the presence of poly(dimethylsiloxane) stabilizers was investigated. It was demonstrated that the dose plays the key role in the progress of the reaction and in the morphology of the resulting polymer. Dispersion polymerization carried out in the presence of mono- and bifunctionalized surfactants gave differently structured polymers. The polymers obtained have been characterized by scanning electron microscopy, solubility tests, and gel permeation chromatography, and the molecular structure has been related to dynamic me…