A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

A finite strain nonlinear human mitral valve model with fluid structure interaction

A simulated human mitral valve under a physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used for characterizing the mechanical behaviour of the mitral valve tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with the measurements from the magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet, and concentrated around the annulus trigons and free edges of the valve leaflets. Those areas are located where the leaflet has the highest curvature. Effects of the chordae tendineae in the material model are studied and the results show that these chordae play an important role in providing a secondary orifice for the flow when valve opens. Although there are some discrepancies to be overcome in future works, our simulations show that the developed computational model is promising in mimicking the in vivo mitral valve dynamics and providing important information that are not obtainable by in vivo measurements. This article is protected by copyright. All rights reserved

Spatial patterns of scour and fill in dryland sand bed streams

Reproduced with permission of the publisher. © 2006 American Geophysical UnionSpatial patterns of scour and fill in two dryland ephemeral stream channels with sandy bed material have been measured with dense arrays of scour chains. Although the depth and areal extent of bed activity increased with discharge, active bed reworking at particular locations within the reaches resulted in downstream patterns of alternate shallower and deeper areas of scour. The variation was such that mean scour depths for individual cross sections varied about the mean for the reach by a factor of 2–4 while the locus of maximum scour traced a sinuous path about the channel centerline. The wavelength of the pattern of scour was about seven times the channel width. During each event, compensating fill returned the streambeds to preflow elevations, indicating that the streams were in approximate steady state over the period of study. Although the patterns of periodically enhanced scour along alternate sides of the channels are consistent with models of periodically reversing helical flow, further work is required to identify the causal relationships between patterns of flow and sediment transport in dryland sand bed channels

Statistical effect in the parton distribution functions of the nucleon

A new and simple statistical approach is performed to calculate the parton distribution functions (PDFs) of the nucleon in terms of light-front kinematic variables. We do not put in any extra arbitrary parameter or corrected term by hand, which guarantees the stringency of our approach. Analytic expressions of the $x$-dependent PDFs are obtained in the whole $x$ region [0,1], and some features, especially the low-$x$ rise, are more agreeable with experimental data than those in some previous instant-form statistical models in the infinite-momentum frame (IMF). Discussions on heavy-flavored PDFs are also presented.Comment: 16 latex pages, 10 figures, to appear in PL

Plum pudding random medium model of biological tissue toward remote microscopy from spectroscopic light scattering

Biological tissue has a complex structure and exhibits rich spectroscopic behavior. There is \emph{no} tissue model up to now able to account for the observed spectroscopy of tissue light scattering and its anisotropy. Here we present, \emph{for the first time}, a plum pudding random medium (PPRM) model for biological tissue which succinctly describes tissue as a superposition of distinctive scattering structures (plum) embedded inside a fractal continuous medium of background refractive index fluctuation (pudding). PPRM faithfully reproduces the wavelength dependence of tissue light scattering and attributes the "anomalous" trend in the anisotropy to the plum and the powerlaw dependence of the reduced scattering coefficient to the fractal scattering pudding. Most importantly, PPRM opens up a novel venue of quantifying the tissue architecture and microscopic structures on average from macroscopic probing of the bulk with scattered light alone without tissue excision. We demonstrate this potential by visualizing the fine microscopic structural alterations in breast tissue (adipose, glandular, fibrocystic, fibroadenoma, and ductal carcinoma) deduced from noncontact spectroscopic measurement

Scaling Separability Criterion: Application To Gaussian States

We introduce examples of three- and four-mode entangled Gaussian mixed states that are not detected by the scaling and Peres-Horodecki separability criteria. The presented modification of the scaling criterion resolves this problem. Also it is shown that the new criterion reproduces the main features of the scaling pictures for different cases of entangled states, while the previous versions lead to completely different outcomes. This property of the presented scheme is evidence of its higher generality.Comment: 7 pages, 4 figure

Information transfer using a single particle path-spin hybrid entangled state

The path-spin entangled state of a single spin-1/2 particle is considered which is generated by using a beam-spitter and a spin-flipper. Using this hybrid entanglement at the level of a single particle as a resource, we formulate a protocol for transferring of the state of an unknown qubit to a distant location. Our scheme is implemented by a sequence of unitary operations along with suitable spin-measurements, as well as by using classical communication between the two spatially separated parties. This protocol, thus, demonstrates the possibility of using intraparticle entanglement as a physical resource for performing information theoretic tasks

Effect of phase fluctuation and dephasing on the dynamics of entanglement generation in a correlated emission laser

A detailed study of the effects of phase fluctuation and dephasing on the dynamics of the entanglement generated from a coherently pumped correlated emission laser is presented. It is found that the time evolution of the entanglement is significantly reliant on the phase fluctuation and dephasing, particularly, at early stages of the lasing process. In the absence of external driving radiation, the degree of entanglement and intensity turns out to attain a maximum value just before starting to exhibit oscillation which dies at longer time scale. However, in case the driving mechanism is on, the oscillatory nature disappears due to the additional induced coherent superposition and the degree of entanglement would be larger at steady state. Moreover, the degree of entanglement as predicted by the logarithmic negativity and the Duan-Giedke-Cirac-Zoller criteria exhibits a similar nature when there is no driving radiation, although such a trend is eroded with increasing strength of the pumping radiation at longer time scale. The other important aspect of the phase fluctuation and dephasing is the possibility of relaxing the time at which the maximum entanglement is detected.Comment: 10 pages, 10 figure

Controllable Entanglement of Lights in a Five-Level System

We analyze the nonlinear optical response of a five-level system under a novel configuration of electro-magnetically induced transparency. We show that a giant Kerr nonlinearity with a relatively large cross-phase modulation coefficient that occurs in such system may be used to produce an efficient photon-photon entanglement. We demonstrate that such photon-photon entanglement is practically controllable and hence facilitates promising applications in quantum information and computation.Comment: 13 pages, 4 figures, 1 column. We have added a section in which the distortion of pulses due to the dispersion is considere

Aggregates of Chemically Functionalized Multiwalled Carbon Nanotubes as Viscosity Reducers

Confinement and surface effects provided by nanoparticles have been shown to produce changes in polymer molecules affecting their macroscopic viscosity. Nanoparticles may induce rearrangements in polymer conformation with an increase in free volume significantly lowering the viscosity. This phenomenon is generally attributed to the selective adsorption of the polymer high molar mass fraction onto nanoparticles surface when the polymer radius of gyration is comparable to the nanoparticles characteristic dimensions. Carbon nanotubes seem to be the ideal candidate to induce viscosity reduction of polymer due to both their high surface-to-volume ratio and their nanometric sizes, comparable to the gyration radius of polymer chains. However, the amount of nanotube in a polymer system is limited by the percolation threshold as, above this limit, the formation of a nanotubes network hinders the viscosity reduction effect. Based on these findings, we have used multiwalled carbon nanotubes MWCNT “aggregates” as viscosity reducers. Our results reveal both that the use of nanotube clusters reduce significantly the viscosity of the final system and strongly increase the nanotube limiting concentration for viscosity hindering. By using hydroxyl and carboxyl functionalized nanotubes, this effect has been rather maximized likely due to the hydrogen bridged stabilization of nanotube aggregates