Censored Glauber Dynamics for the mean field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on $n$ vertices, known as the Curie-Weiss Model. It is well known that at high temperature ($\beta < 1$) the mixing time is $\Theta(n\log n)$, whereas at low temperature ($\beta > 1$) it is $\exp(\Theta(n))$. Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed $\beta > 1$, the mixing-time of this model is $\Theta(n\log n)$, analogous to the high-temperature regime of the original dynamics. Furthermore, they showed \emph{cutoff} for the original dynamics for fixed $\beta<1$. The question whether the censored dynamics also exhibits cutoff remained unsettled. In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Currie-Weiss model. Namely, we found a scaling window of order $1/\sqrt{n}$ around the critical temperature $\beta_c=1$, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging. In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if $\beta = 1 + \delta$ for some $\delta > 0$ with $\delta^2 n \to \infty$, then the mixing-time has order $(n / \delta)\log(\delta^2 n)$. The cutoff constant is $(1/2+[2(\zeta^2 \beta / \delta - 1)]^{-1})$, where $\zeta$ is the unique positive root of $g(x)=\tanh(\beta x)-x$, and the cutoff window has order $n / \delta$.Comment: 55 pages, 4 figure

Higgs pair production in the MSSM with explicit CP violation

In the minimal supersymmetric standard model with explicit CP violation, associated production of the lightest Higgs boson with heavier ones is analyzed. Due to explicit CP violation, the Higgs bosons are no longer CP eigenstates so that both of the heavy Higgs bosons contribute to the process. While the radiative corrections in the Higgs sector turn out to be quite important, the vertex radiative corrections remain small as in the CP conserving theory.Comment: 5 pp, 5 figs, Talk at Valencia 99, Valencia, Spain, May 3-8, 199

Condenser-free contrast methods for transmitted-light microscopy

Phase contrast microscopy allows the study of highly transparent yet detail-rich specimens by producing intensity contrast from phase objects within the sample. Presented here is a generalized phase contrast illumination schema in which condenser optics are entirely abrogated, yielding a condenser- free yet highly effective method of obtaining phase contrast in transmitted-light microscopy. A ring of light emitting diodes (LEDs) is positioned within the light-path such that observation of the objective back focal plane places the il- luminating ring in appropriate conjunction with the phase ring. It is demonstrated that true Zernike phase contrast is obtained, whose geometry can be flexibly manipulated to provide an arbitrary working distance between illuminator and sample. Condenser-free phase contrast is demonstrated across a range of magnifications (4–100×), numerical apertures (0.13–1.65NA) and conventional phase positions. Also demonstrated is condenser-free darkfield microscopy as well as combinatorial contrast including Rheinberg illumination and simultaneous, colour-contrasted, brightfield, darkfield and Zernike phase contrast. By providing enhanced and arbitrary working space above the preparation, a range of concurrent imaging and electrophysiological techniques will be technically facilitated. Condenser-free phase contrast is demonstrated in conjunction with scanning ion conductance microscopy (SICM), using a notched ring to admit the scanned probe. The compact, versatile LED illumination schema will further lend itself to novel next-generation transmitted-light microscopy designs. The condenser-free illumination method, using rings of independent or radially-scanned emitters, may be exploited in future in other electromagnetic wavebands, including X-rays or the infrared

Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Horizontal and vertical movements of starry smooth-hound Mustelus asterias in the northeast Atlantic

Commercial landings of starry smooth-hound Mustelus asterias in northern European seas are increasing, whilst our knowledge of their ecology, behaviour and population structure remains limited. M. asterias is a widely distributed demersal shark, occupying the waters of the southern North Sea and Irish Sea in the north, to at least the southern Bay of Biscay in the south, and is seasonally abundant in UK waters. There are no species-specific management measures for the northeast Atlantic stock, and the complexity of its population structure is not yet fully understood. To address this issue, we deployed both mark-recapture and electronic tags on M. asterias to gain novel insights into its horizontal and vertical movements. Our data suggest that the habitat use of M. asterias changes on a seasonal basis, with associated changes in geographical distribution, depth utilisation and experienced temperature. We report the first direct evidence of philopatry for this species, and also provide initial evidence of sex-biased dispersal and potential metapopulation-like stock structuring either side of the UK continental shelf. Investigations of finer-scale vertical movements revealed clear diel variation in vertical activity. The illustrated patterns of seasonal space-use and behaviour will provide important information to support the stock assessment process and will help inform any future management options

Supersymmetric Benchmarks with Non-Universal Scalar Masses or Gravitino Dark Matter

We propose and examine a new set of benchmark supersymmetric scenarios, some of which have non-universal Higgs scalar masses (NUHM) and others have gravitino dark matter (GDM). The scalar masses in these models are either considerably larger or smaller than the narrow range allowed for the same gaugino mass m_{1/2} in the constrained MSSM (CMSSM) with universal scalar masses m_0 and neutralino dark matter. The NUHM and GDM models with larger m_0 may have large branching ratios for Higgs and/or $Z$ production in the cascade decays of heavier sparticles, whose detection we discuss. The phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10^4 seconds in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino \chi, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton {\tilde \tau}_1, with a lifetime between ~ 10^4 and 3 X 10^6 seconds. Every supersymmetric cascade would end in a {\tilde \tau}_1, which would have a distinctive time-of-flight signature. Slow-moving {\tilde \tau}_1's might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the {\tilde \tau}_1 lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.Comment: 52 pages LaTeX, 13 figure

Scalar and Pseudoscalar Higgs Boson Plus One Jet Production at the LHC and Tevatron

The production of the Standard Model (SM) Higgs boson (H) in association with a jet is compared with that of the lightest scalar Higgs boson (h^0) and the pseudoscalar Higgs boson (A^0) of the Minimal Supersymmetric Model (MSSM) at both the CERN Large Hadron Collider (LHC) and the Fermilab Tevatron. We include both top and bottom quark loops to lowest order in QCD and investigate the limits of zero quark mass and infinite quark mass.Comment: 14 pages, REVTeX4, 14 eps figures v2: Version accepted for publication in PR

Associated production of light gravitinos in e^+e^- and e^-\gamma collisions

Light gravitino productions in association with a neutralino (selectron) in e^+e^- (e^-\gamma) collisions are restudied in a scenario that the lightest supersymmetric particle is a gravitino and the produced neutralino (selectron) promptly decays into a photon (electron) and a gravitino. We explicitly give the helicity amplitudes for the production processes by using the effective goldstino interaction Lagrangian, and present the cross sections with different collision energies and mass spectra. We also examine selection efficiencies by kinematical cuts and beam polarizations for the signal and background processes, and show that the energy and angular distributions of the photon (electron) can explore the mass of the t-channel exchange particle as well as the mass of the decaying particle at a future e^+e^- (e^-\gamma) collider.Comment: 12 pages, 12 figures, 4 tables; references added, version to appear in EPJ

Fermionic partner of Quintessence field as candidate for dark matter

Quintessence is a possible candidate for dark energy. In this paper we study the phenomenologies of the fermionic partner of Quintessence, the Quintessino. Our results show that, for suitable choices of the model parameters, the Quintessino is a good candidate for cold or warm dark matter. In our scenario, dark energy and dark matter of the Universe are connected in one chiral superfield.Comment: 4 pages, 3 figures, version to appear in PR