Generalized Smoluchowski equation with correlation between clusters

In this paper we compute new reaction rates of the Smoluchowski equation which takes into account correlations. The new rate K = KMF + KC is the sum of two terms. The first term is the known Smoluchowski rate with the mean-field approximation. The second takes into account a correlation between clusters. For this purpose we introduce the average path of a cluster. We relate the length of this path to the reaction rate of the Smoluchowski equation. We solve the implicit dependence between the average path and the density of clusters. We show that this correlation length is the same for all clusters. Our result depends strongly on the spatial dimension d. The mean-field term KMFi,j = (Di + Dj)(rj + ri)d-2, which vanishes for d = 1 and is valid up to logarithmic correction for d = 2, is the usual rate found with the Smoluchowski model without correlation (where ri is the radius and Di is the diffusion constant of the cluster). We compute a new rate: the correlation rate K_{i,j}^{C} (D_i+D_j)(r_j+r_i)^{d-1}M{\big(\frac{d-1}{d_f}}\big) is valid for d \leq 1(where M(\alpha) = \sum+\infty i=1i\alphaNi is the moment of the density of clusters and df is the fractal dimension of the cluster). The result is valid for a large class of diffusion processes and mass radius relations. This approach confirms some analytical solutions in d 1 found with other methods. We also show Monte Carlo simulations which illustrate some exact new solvable models

An in vivo control map for the eukaryotic mRNA translation machinery

Rate control analysis defines the in vivo control map governing yeast protein synthesis and generates an extensively parameterized digital model of the translation pathway. Among other non-intuitive outcomes, translation demonstrates a high degree of functional modularity and comprises a non-stoichiometric combination of proteins manifesting functional convergence on a shared maximal translation rate. In exponentially growing cells, polypeptide elongation (eEF1A, eEF2, and eEF3) exerts the strongest control. The two other strong control points are recruitment of mRNA and tRNAi to the 40S ribosomal subunit (eIF4F and eIF2) and termination (eRF1; Dbp5). In contrast, factors that are found to promote mRNA scanning efficiency on a longer than-average 5′untranslated region (eIF1, eIF1A, Ded1, eIF2B, eIF3, and eIF5) exceed the levels required for maximal control. This is expected to allow the cell to minimize scanning transition times, particularly for longer 5′UTRs. The analysis reveals these and other collective adaptations of control shared across the factors, as well as features that reflect functional modularity and system robustness. Remarkably, gene duplication is implicated in the fine control of cellular protein synthesis

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be appeared in Phys. Rev. Let

Milagrito Detection of TeV Emission from Mrk 501

The Milagro water Cherenkov detector near Los Alamos, New Mexico, has been operated as a sky monitor at energies of a few TeV between February 1997 and April 1998. Serving as a test run for the full Milagro detector, Milagrito has taken data during the strong and long-lasting 1997 flare of Mrk 501. We present results from the analysis of Mrk 501 and compare the excess and background rates with expectations from the detector simulations.Comment: 4 pages, submitted to XXVI International Cosmic Ray Conference, Salt Lake Cit

Results from the Milagrito experiment

The Milagro water Cherenkov detector near Los Alamos, New Mexico is the first air shower detector capable of continuously monitoring the sky at energies between 500 GeV and 20 TeV. Preliminary results of the Milagro experiment are presented. A predecessor of the Milagro detector, Milagrito, was operational from February 1997 to May 1998. Milagrito consisted of 228 8″ photomultiplier tubes (PMTs) arranged in a grid with a 2.8 meter spacing and submerged in 1–2 meters of water. During its operation, Milagrito collected in excess of 9 billion events with a median energy of about 3 TeV. The detector’s sensitivity extends below 1 TeV for showers from near zenith. The results of an all sky search for the Milagrito data for both transient and DC sources will be presented, including the Crab Nebula and active galaxies Markarian 501 and 421, which are known sources of TeV gamma-rays. Also presented will be a study of the TeV emission from gamma ray bursts (GRBs) in Milagrito’s field of view detected by the BATSE experiment on the Compton Gamma-Ray Observatory

First Results of a Study of TeV Emission from GRBs in Milagrito

Milagrito, a detector sensitive to gamma-rays at TeV energies, monitored the northern sky during the period February 1997 through May 1998. With a large field of view and high duty cycle, this instrument was used to perform a search for TeV counterparts to gamma-ray bursts. Within the Milagrito field of view 54 gamma-ray bursts at keV energies were observed by the Burst And Transient Satellite Experiment (BATSE) aboard the Compton Gamma-Ray Observatory. This paper describes the results of a preliminary analysis to search for TeV emission correlated with BATSE detected bursts. Milagrito detected an excess of events coincident both spatially and temporally with GRB 970417a, with chance probability $2.8 \times 10^{-5}$ within the BATSE error radius. No other significant correlations were detected. Since 54 bursts were examined the chance probability of observing an excess with this significance in any of these bursts is $1.5 \times 10^{-3}$. The statistical aspects and physical implications of this result are discussed.Comment: 6 pages, 5 figures, to appear in "GeV-TeV Astrophysics: Toward a Major Atmospheric Cherenkov Telescope VI," Snowbird, Utah (August, 1999