Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Ho\v{r}ava-Lifshitz gravity. It is shown that, when the parameter of Ho\v{r}ava-Lifshitz gravity $\omega\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Ho\v{r}ava-Lifshitz gravity.Comment: 9 pages, no figure

Localization properties of the anomalous diffusion phase x tμx ~ t^{\mu} in the directed trap model and in the Sinai diffusion with bias

We study the anomalous diffusion phase $x ~ t^{\mu}$ with $0<\mu<1$ which exists both in the Sinai diffusion at small bias, and in the related directed trap model presenting a large distribution of trapping time $p(\tau) \sim 1/\tau^{1+\mu}$. Our starting point is the Real Space Renormalization method in which the whole thermal packet is considered to be in the same renormalized valley at large time : this assumption is exact only in the limit $\mu \to 0$ and corresponds to the Golosov localization. For finite $\mu$, we thus generalize the usual RSRG method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows to compute exact series expansions in $\mu$ of all observables : at order $\mu^n$, it is sufficient to consider a spreading of the thermal packet onto at most $(1+n)$ traps in each sample, and to average with the appropriate measure over the samples. For the directed trap model, we show explicitly up to order $\mu^2$ how to recover the diffusion front, the thermal width, and the localization parameter $Y_2$. We moreover compute the localization parameters $Y_k$ for arbitrary $k$, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias, by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models.Comment: 33 pages, 3 eps figure

Measurement of open charm production in dd+Au collisions at sNN\sqrt{s_{NN}}=200 GeV

We present the first comprehensive measurement of $D^{0}, D^{+}, D^{*+}$ and their charge conjugate states at mid-rapidity in $d$+Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV using the STAR TPC. The directly measured open charm multiplicity distribution covers a broad transverse momentum region of 0$<p_{T}<11$ GeV/$c$. The measured $dN/dy$ at mid-rapidity for $D^{0}$ is $0.0265\pm 0.0036 (stat.) \pm 0.0071 (syst.)$ and the measured $D^{*+}/D^{0}$ and $D^{+}/D^{0}$ ratios are approximately equal with a magnitude of $0.40\pm 0.09(stat.) \pm 0.13(syst.)$. The total $c\bar{c}$ cross section per nucleon-nucleon collision extracted from this study is $1.18 \pm 0.21(stat.) \pm 0.39(syst.)$mb. The direct measurement of open charm production is consistent with STAR single electron data. This cross section is higher than expectations from PYTHIA and other pQCD calculations. The measured $p_{T}$ distribution is harder than the pQCD prediction using the Peterson fragmentation function.Comment: Quark Matter 2004 Proceeding

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Non-identical particle correlations in 130 and 200 AGeV collisions at STAR

STAR has performed a correlation analyses of pion-kaon and pion-proton pairs for sqrt(s_NN)=130 AGeV and sqrt(s_NN)=200 AGeV and kaon-proton, proton-Lambda and pion-Cascade pairs for AuAu collisions sqrt(s_NN)=200 AGeV. They show that average emission space-time points of pions, kaons and protons are not the same. These asymmetries are interpreted as a consequence of transverse radial expansion of the system; emission time differences explain only part of the asymmetry. Therefore our measurements independently confirm the existence of transverse radial flow. Furthermore, correlations of strange hyperons is investigated by performing proton-Lambda and pion-Cascade analyses, giving estimates of source size at high m_{T}. The strong interaction potential between (anti-)proton and lambda as well as kaon and proton is investigated.Comment: 5 pages, 3 figures, Quark Matter 04 proceedings, submitted to J. Phys. G: Nucl. Phy

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio