The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.Comment: 8 pages, 5 figures, latex, include europhys.sty and euromacr.te

A medieval fallacy: the crystalline lens in the center of the eye.

ObjectiveTo determine whether, as most modern historians have written, ancient Greco-Roman authors believed the crystalline lens is positioned in the center of the eye.BackgroundHistorians have written that statements about cataract couching by Celsus, or perhaps Galen of Pergamon, suggested a centrally located lens. Celsus specifically wrote that a couching needle placed intermediate between the corneal limbus and the lateral canthus enters an empty space, presumed to represent the posterior chamber.MethodsAncient ophthalmic literature was analyzed to understand where these authors believed the crystalline lens was positioned. In order to estimate where Celsus proposed entering the eye during couching, we prospectively measured the distance from the temporal corneal limbus to the lateral canthus in 30 healthy adults.ResultsRufus of Ephesus and Galen wrote that the lens is anterior enough to contact the iris. Galen wrote that the lens equator joins other ocular structures at the corneoscleral junction. In 30 subjects, half the distance from the temporal corneal limbus to the lateral canthus was a mean of 4.5 mm (range: 3.3-5.3 mm). Descriptions of couching by Celsus and others are consistent with pars plana entry of the couching needle. Anterior angulation of the needle would permit contact of the needle with the lens.ConclusionAncient descriptions of anatomy and couching do not establish the microanatomic relationships of the ciliary region with any modern degree of accuracy. Nonetheless, ancient authors, such as Galen and Rufus, clearly understood that the lens is located anteriorly. There is little reason to believe that Celsus or other ancient authors held a variant understanding of the anatomy of a healthy eye. The notion of the central location of the lens seems to have arisen with Arabic authors in 9th century Mesopotamia, and lasted for over 7 centuries

Remote preparation of arbitrary ensembles and quantum bit commitment

The Hughston-Jozsa-Wootters theorem shows that any finite ensemble of quantum states can be prepared "at a distance", and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules. In this paper, we prove a generalized HJW theorem for arbitrary ensembles of states on a C*-algebra. We then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems, and quantum systems with Abelian superselection rules.Comment: 21 pages, LaTeX. Version 2: Proofs expanded and made more self-contained; added an example of a bit commitment protocol with continuous ensemble

Instrumented Lumbar Corpectomy and Spinal Reconstruction Comparing rhBMP-2/Compression-Resistant Matrix, rhBMP-2/Absorbable Collagen Sponge/Ceramic Granules Mixture, and Autograft in Two Different Devices: A Study in Sheep

Study Design. Fusion success with rhBMP-2 and autograft in titanium or PEEK corpectomy devices was evaluated in a sheep lumbar corpectomy model. The 6 treatment groups included titanium mesh or PEEK corpectomy devices filled with rhBMP-2 on a compression-resistant matrix (CRM) carrier; rhBMP-2 in a morselized absorbable collagen sponge (ACS) carrier combined with resorbable ceramic granules; and autograft. Objective. The aim of this study was to determine fusion rates associated with 2 different preparations of rhBMP-2 as well as autograft in an instrumented ovine lumbar corpectomy model 6 months postoperatively. Summary of Background Data. Vertebral reconstruction with corpectomy devices requires bone graft. Bone graft substitutes have the potential to avoid a second operation, donor site pain, and attendant morbidity associated with autograft. Methods. Twenty-four sheep in 6 treatment groups underwent lumbar corpectomy via a retroperitoneal trans-psoas approach. Spines were reconstructed with autograft, rhBMP-2 on a CRM, or rhBMP-2 on an ACS mixed with ceramic granules. Grafting materials were placed in either a titanium mesh or PEEK conduit in spines with internal fixation. Computed tomographic (CT) scans were evaluated for fusion. Undecalcified histology was used to evaluate for fusion as well as the amount and extent of graft incorporation and graft resorption. Results. Regardless of corpectomy device used, rhBMP-2/CRM or rhBMP-2/ACS with MASTERGRAFT resulted in a 100% fusion rate. The autograft group had a lower (75%) radiographic fusion rate. Using either preparation of rhBMP-2 resulted in the length of the defect filling with solid bone. Autograft fragments and ceramic granules were incorporated into the fusion masses with much of the ceramic granules being resorbed by 6 months. Conclusion. Both of the rhBMP-2 formulations have the potential to effect bony fusion and vertebral reconstruction within the corpectomy devices

Energy conditions for a generally coupled scalar field outside a reflecting sphere

We calculate the stress-energy tensor for a scalar field with general curvature coupling, outside a perfectly reflecting sphere with Dirichlet boundary conditions. For conformal coupling we find that the null energy condition is always obeyed, and therefore the averaged null energy condition (ANEC) is also obeyed. Since the ANEC is independent of curvature coupling, we conclude that the ANEC is obeyed for scalar fields with any curvature coupling in this situation. We also show how the spherical case goes over to that of a flat plate as one approaches the sphere.Comment: Accepted for publication in Phys. Rev.

Random field Ising systems on a general hierarchical lattice: Rigorous inequalities

Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These inequalities lead to upper bounds on the crossover exponents $\{\phi_i\}$.Comment: LaTeX, 13 pages, figs. 1a,1b,2. To be published in PR

TE Wave Measurement and Modeling

In the TE wave method, microwaves are coupled into the beam-pipe and the effect of the electron cloud on these microwaves is measured. An electron cloud (EC) density can then be calculated from this measurement. There are two analysis methods currently in use. The first treats the microwaves as being transmitted from one point to another in the accelerator. The second more recent method, treats the beam-pipe as a resonant cavity. This paper will summarize the reasons for adopting the resonant TE wave analysis as well as give examples from CESRTA and DA{\Phi}NE of resonant beam-pipe. The results of bead-pull bench measurements will show some possible standing wave patterns, including a cutoff mode (evanescent) where the field decreases exponentially with distance from the drive point. We will outline other recent developments in the TE wave method including VORPAL simulations of microwave resonances, as well as the simulation of transmission in the presence of both an electron cloud and magnetic fields.Comment: Presented at ECLOUD'12: Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects, La Biodola, Isola d'Elba, Italy, 5-9 June 2012; CERN-2013-002, pp. 193-20

The nature of the long time decay at a second order transition point

We show that at a second order phase transition, of \phi^4 like system, a necessary condition for streched exponential decay of the time structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of the structure factor is obtained and shown to yield stretched exponential decay under very reasonable conditions.Comment: 7 page

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Steep sharp-crested gravity waves on deep water

A new type of steady steep two-dimensional irrotational symmetric periodic gravity waves on inviscid incompressible fluid of infinite depth is revealed. We demonstrate that these waves have sharper crests in comparison with the Stokes waves of the same wavelength and steepness. The speed of a fluid particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let