Pseudo-random number generator based on discrete-space chaotic map

This paper describes an efficient method to predict the nonlinear steady-state response of a complex structure with multi-scattered friction contacts. The contact friction force is equivalent to additional stiffness and damping based on optimal approximation theory, and as a consequence, the computation is simplified greatly by the linearization for a nonlinear system. In order to obtain accurate pressure distribution on the contact interfaces, the dynamic contact normal pressure is obtained by the equivalent static analysis which is validated for most engineering cases. Considering the complex procedure to determine the transformation between two different contact states, the differential forms of friction force are given to solve the tangential force accurately under the complex movement of interfaces. The approaches developed in this paper are particularly suitable to solve the dynamic response of large-scale structures with local contact nonlinearities. The entire procedure to calculate the steady-state response of a finite element model with a large number of degrees of freedom is demonstrated taking the blades with underplatform dampers as an example. The method is proved to be accurate and efficient; in particular, it does not suffer convergence problem in the allowable range of precision error, which exhibits remarkable potential engineering application values.     

Structural and diffusion characterizations of steam-stable mesostructured zeolitic UL-ZSM-5 materials

A series of mesoporous UL-ZSM-5 materials (Si/Al = 50) with different micro- and mesoporosity as well as crystallinity was prepared following the procedure proposed in one of our recent studies (Trong-On, D.; Kaliaguine, S. Angew. Chem. Int. Ed. 2001, 40, 3248-3251. Trong-On, D.; Kaliaguine, S. U.S. Patent 6,669,924, B1, 2003). These materials have zeolitic structure in the form of nanoparticles intergrown in the walls of the amorphous wormhole-like aluminosilicate mesopores of Al-Meso-50, which was used as a precursor in the synthesis. The structure, crystallinity, and textural properties of the synthesized materials, as well as a reference ZSM-5 zeolite sample, were determined by X-ray diffraction (XRD), transmission electron microscopy (TEM)/scanning electron microscoy (SEM) analyses, Fourier transform infrared spectroscopy (FTIR), 27Al magic angle spinning (MAS) nuclear magnetic resonance (NMR), and nitrogen adsorption/desorption techniques. The acid properties were examined by FTIR of adsorbed pyridine. UL-ZSM-5 materials were shown to be highly hydrothermally stable. The diffusion of two C7 hydrocarbons, i.e., n-heptane and toluene, in four UL-ZSM-5 materials with different microporosities, related acidities, and crystallinities were investigated using the zero-length column (ZLC) method. Furthermore, the wormhole-like mesostructured aluminosilicate precursor (Al-Meso-50) and a reference MFI zeolite sample were also investigated using the same technique. A theoretical model considering a combination of mesopore diffusion (with surface slip in the main channels) with an activated, mainly surface diffusion mechanism in the intrawall biporous structure, was proposed and employed to interpret the experimental ZLC results. A classical Knudsen type of diffusion was replaced by an activated surface slip type of diffusion mechanism in the mesopores. The transport of n-heptane in UL-ZSM-5 materials was found to be mainly controlled by mesopore diffusion in the main-channel structure, while that of toluene was dominated by the intrawall diffusion process. Diffusion activation energies of n-heptane are about 2 times higher in comparison to toluene, which has a larger kinetic diameter. The main mesopore channel structure seems to appreciably contribute to the overall mass transport. Furthermore, the effect of hydrothermal treatment (20% steam at 800 degrees C for 24 h) on the diffusion of these two sorbates on UL-ZSM-5 materials was also evaluated.     

Surface-enhanced Raman scattering on molecular self-assembly in nanoparticle-hydrogel composite

Surface-enhanced Raman scattering has been applied to study weak intermolecular interactions between small organic gelling molecules involved in the silver nanoparticle-hydrogel composite formation. Assembly and disassembly of the gelator molecules in close vicinity to embedded silver nanoparticles were followed by changes in Raman intensity of the amide II and carboxyl vibrational bands, whereas the strength of the bands related to benzene modes remained constant. This implied that the gelator molecules were strongly attached to the silver particles through the benzene units, while participating in gel structure organization by intermolecular hydrogen bonding between oxalyl amide and carboxyl groups.     

Stray field magnetic resonance tomography using ferromagnetic spheres

The methodology for obtaining two- and three-dimensional magnetic resonance images by using azimuthally symmetric dipolar magnetic fields from ferromagnetic spheres is described. We utilize the symmetric property of a geometric sphere in the presence of a large externally applied magnetic field to demonstrate that a complete two- or three-dimensional structured rendering of a sample can be obtained without the motion of the sample relative to the sphere. Sequential positioning of the integrated sample-sphere system in an external magnetic field at various angular orientations provides all the required imaging slices for successful computerized tomographic image reconstruction. The elimination of the requirement to scan the sample relative to the ferromagnetic tip in this imaging protocol is a potentially valuable simplification compared to previous scanning probe magnetic resonance imaging proposals.     

Hilbert Lattice Equations

There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet’s E_A{\mathcal{E}_A}, Godowski, Mayet–Godowski, and Mayet’s E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet–Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered. Finally, we show some new results on the Godowski lattices characterising the third class of equations.     

Minimal quantum logic with merged implications

It is shown that the property of orthomodularity can be interpreted as a particular reduction of the operations of implication to the relation of implication, and a physical interpretation of the result is given.     

Van Kampen’s embedding obstruction for discrete groups

We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the n-fold product of nonabelian free groups cannot act properly discontinuously on ℝ^{2 n −1}. Oblatum 19-I-2001 & 29-V-2002?Published online: 5 September 2002 RID="*" ID="*"All three authors gratefully acknowledge the support by the National Science Foundation.     

Quantum Logic for Quantum Computers

The following results obtained within a project of finding the algebra of statesin a general-purpose quantum computer are reported: (1) All operations of anorthomodular lattice, including the identity, are fivefold-defined; (2) there arenonorthomodular models for both quantum and classical logics; (3) there is afour-variable orthoarguesian lattice condition which contains all known orthoarguesianlattice conditions including six- and five-variable ones. Repercussions to quantumcomputers operating as quantum simulators are discussed.     

An existence result for nonisothermal immiscible incompressible 2‐phase flow in heterogeneous porous media

In the present article, we study the temperature effects on two‐phase immiscible incompressible flow through a porous medium. The mathematical model is given by a coupled system of 2‐phase flow equations and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy‐Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation; ie, the saturation of one phase, the pressure of the second phase, and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we show the existence of weak solutions with the help of an appropriate regularization and a time discretization. We use suitable test functions to obtain a priori estimates. We prove a new compactness result to pass to the limit in nonlinear terms.     

How Secure Are Two-Way Ping-Pong and LM05 QKD Protocols under a Man-in-the-Middle Attack?

We consider a man-in-the-middle attack on two-way quantum key distribution ping-pong and LM05 protocols in which an eavesdropper copies all messages in the message mode, while being undetectable in the mode. Under the attack there is therefore no disturbance in the message mode and the mutual information between the sender and the receiver is always constant and equal to one and messages copied by the eavesdropper are always genuine. An attack can only be detected in the control mode but the level of detection at which the protocol should be aborted is not defined. We examine steps of the protocol to evaluate its security and find that the protocol should be redesigned. We also compare it with the security of a one-way asymmetric BB84-like protocol in which one basis serves as the message mode and the other as the control mode but which does have the level of detection at which the protocol should be aborted defined.