Slicing Sets and Measures, and the Dimension of Exceptional Parameters

We consider the problem of slicing a compact metric space \Omega with sets of the form \pi_{\lambda}^{-1}\{t\}, where the mappings \pi_{\lambda} \colon \Omega \to \R, \lambda \in \R, are \emph{generalized projections}, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that \Omega has Hausdorff dimension strictly greater than one, what is the dimension of the 'typical' slice \pi_{\lambda}^{-1}{t}, as the parameters \lambda and t vary. In the special case of the mappings \pi_{\lambda} being orthogonal projections restricted to a compact set \Omega \subset \R^{2}, the problem dates back to a 1954 paper by Marstrand: he proved that for almost every \lambda there exist positively many $t \in \R$ such that \dim \pi_{\lambda}^{-1}{t} = \dim \Omega - 1. For generalized projections, the same result was obtained 50 years later by J\"arvenp\"a\"a, J\"arvenp\"a\"a and Niemel\"a. In this paper, we improve the previously existing estimates by replacing the phrase 'almost all \lambda' with a sharp bound for the dimension of the exceptional parameters.Comment: 31 pages, three figures; several typos corrected and large parts of the third section rewritten in v3; to appear in J. Geom. Ana

Spin-Orbit Effects in the Excitation of Proton and Neutron States in the (p,p') Reaction at 160 MeV, 120 MeV, and 95 MeV

Supported by the National Science Foundation and Indiana Universit

Pre-main-sequence population in NGC 1893 region

In this paper we continued our efforts to understand the star formation scenario in and around the young cluster NGC 1893. We used a sample of the young stellar sources (YSOs) identified on the basis of multiwavelength data (optical, near-infrared (NIR), mid-infrared (MIR) and X-ray) to study the nature of YSOs associated with the region. The identified YSOs show an age spread of ~ 5 Myr. The YSOs located near the nebulae at the periphery of the cluster are relatively younger in comparison to those located within the cluster region. The present results are in accordance with those obtained by us in previous studies. Other main results from the present study are: 1) the fraction of disk bearing stars increases towards the periphery of the cluster; 2) there is an evidence supporting the notion that the mechanisms for disk dispersal operate less efficiently for low-mass stars; 3) the sample of Class II sources is found to be relatively older in comparison to that of Class III sources. A comparison of various properties of YSOs in the NGC 1893 region with those in the Tr 37/ IC 1396 region is also discussed.Comment: Accepted for publication in New Astronom

Tunable variation of optical properties of polymer capped gold nanoparticles

Optical properties of polymer capped gold nanoparticles of various sizes (diameter 3-6 nm) have been studied. We present a new scheme to extract size dependent variation of total dielectric function of gold nanoparticles from measured UV-Vis absorption data. The new scheme can also be used, in principle, for other related systems as well. We show how quantum effect, surface atomic co - ordination and polymer - nanoparticle interface morphology leads to a systematic variation in inter band part of the dielectric function of gold nanoparticles, obtained from the analysis using our new scheme. Careful analysis enables identification of the possible changes to the electronic band structure in such nanoparticles.Comment: 13 pages,7 figures, 1 tabl

Coupled influences of particle shape, surface property and flow hydrodynamics on rod-shaped colloid transport in porous media

Hypothesis: Natural or engineered colloidal particles are often non-spherical in shape. In contrast to the widely-used “homogeneous sphere” assumption, the non-spherical particle shape is expected to alter particle–fluid-surface interactions, which in turn affect particle transport and retention. Experiments and Simulations: Polystyrene microspheres were stretched to rod-shaped particles of two aspect ratios (2:1, 6:1). The transport and retention behaviors of rods versus spheres were investigated in packed quartz sand columns and impinging jet systems. In parallel, a 3D trajectory model was employed to simulate particle translation and rotation, and to elucidate the role and underlying mechanisms of particle shape impact on transport. Findings: Rods were observed to undergo rotating and tumbling motions in response to fluid shear from experiments and simulations. However, no distinct retention trends between rods and spheres were observed from column studies, despite BSA-coating on particles, Fe-coating on sand or velocity change. This was primarily due to the super-hydrophobic nature of colloid surfaces acquired from stretching process, which in hydrophilic sand columns, dominated particle–surface charge interactions. Simulations using colloids with randomly distributed charge patches qualitatively produced the observed insensitivity in retention respecting aspect ratio under low charge coverage (<30%). Hence, particle shape influences were strongly coupled with colloid surface properties and flow hydrodynamics

Giant magnetothermopower of magnon-assisted transport in ferromagnetic tunnel junctions

We present a theoretical description of the thermopower due to magnon-assisted tunneling in a mesoscopic tunnel junction between two ferromagnetic metals. The thermopower is generated in the course of thermal equilibration between two baths of magnons, mediated by electrons. For a junction between two ferromagnets with antiparallel polarizations, the ability of magnon-assisted tunneling to create thermopower $S_{AP}$ depends on the difference between the size $\Pi_{\uparrow, \downarrow}$ of the majority and minority band Fermi surfaces and it is proportional to a temperature dependent factor $(k_{B}T/\omega_{D})^{3/2}$ where $\omega_{D}$ is the magnon Debye energy. The latter factor reflects the fractional change in the net magnetization of the reservoirs due to thermal magnons at temperature $T$ (Bloch's $T^{3/2}$ law). In contrast, the contribution of magnon-assisted tunneling to the thermopower $S_P$ of a junction with parallel polarizations is negligible. As the relative polarizations of ferromagnetic layers can be manipulated by an external magnetic field, a large difference $\Delta S = S_{AP} - S_P \approx S_{AP} \sim - (k_B/e) f (\Pi_{\uparrow},\Pi_{\downarrow}) (k_BT/\omega_{D})^{3/2}$ results in a magnetothermopower effect. This magnetothermopower effect becomes giant in the extreme case of a junction between two half-metallic ferromagnets, $\Delta S \sim - k_B/e$.Comment: 9 pages, 4 eps figure

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

Testing "microscopic" theories of glass-forming liquids

We assess the validity of "microscopic" approaches of glass-forming liquids based on the sole k nowledge of the static pair density correlations. To do so we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while disp laying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhausti ve, and we have not tested the effect of adding corrections by including for instance three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowd own of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by "microscopic" appr oaches only requiring the static pair density correlations as nontrivial input.Comment: 10 pages, 7 figs; Accepted to EPJE Special Issue on The Physics of Glasses. Arxiv version contains an addendum to the appendix which does not appear in published versio