scholarly journals Steady-state joint distribution for first-order stochastic reaction kinetics

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Youming Li ◽  
Da-Quan Jiang ◽  
Chen Jia
1995 ◽  
Vol 60 (10) ◽  
pp. 1621-1633 ◽  
Author(s):  
Stanislav Böhm ◽  
Mojmír Adamec ◽  
Stanislav Nešpůrek ◽  
Josef Kuthan

Molecular geometries of 2,4,4,6-tetraphenyl-4H-pyran (Ia), 4,4-(biphenyl-2,2e-diyl)-2,6-diphenyl-4H-pyran (Ib) and their heterocyclic isomers II-V were optimized by the PM3 method and used for the calculation of electronic absorption spectra by the CNDO/S-CI procedure. Comparison of the theoretical data with experimental UV-VIS absorption spectra made possible to select hypervalent molecules IIIa, IIIb, IVa and IVb being responsible for the photocolouration of 4H-pyrans Ia, Ib, while compounds Va, Vb, VI and VII come into account as possible photodegradation products. The bleaching process of the UV illuminated compound Ia is analyzed in terms of dispersive first-order reaction kinetics.


2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Tommaso Canneti ◽  
Aldo L. Cotrone

Abstract Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of $$ Dq\hbox{-} \overline{D}q $$ Dq ‐ D ¯ q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto $$ D4\hbox{-} D8\hbox{-} \overline{D}8 $$ D 4 ‐ D 8 ‐ D ¯ 8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.


1992 ◽  
Vol 26 (9-11) ◽  
pp. 1995-1998 ◽  
Author(s):  
B. M. Peyton ◽  
W. G. Characklis

In predictive biofilm modeling, the detachment rate coefficient may be the most sensitive variable affecting both the predicted rate and the extent of biofilm accumulation. At steady state the detachment rate must be equal to the net growth rate in the biofilm. In systems where organic carbon is growth-limiting, the substrate carbon utilization rate determines the net biomass production rate and, therefore, the steady state biomass detachment rate. Detachment rates, first order with biofilm thickness, fit the experimental data well, but are not predictive since the coefficients must be determined experimentally.


1995 ◽  
Vol 128 (4) ◽  
pp. 549-561 ◽  
Author(s):  
R N Ghosh ◽  
F R Maxfield

We have previously characterized the trafficking of transferrin (Tf) through HEp2 human carcinoma cells (Ghosh, R. N., D. L. Gelman, and F. R. Maxfield, 1994. J. Cell Sci. 107:2177-2189). Early endosomes in these cells are comprised of both sorting endosomes and recycling compartments, which are distinct separate compartments. Endocytosed Tf initially appears in punctate sorting endosomes that also contain recently endocytosed LDL. After short loading pulses, Tf rapidly sorts from LDL with first-order kinetics (t1/2 approximately 2.5 min), and it enters the recycling compartment before leaving the cell (t1/2 approximately 7 min). Here, we report a second, slower rate for Tf to leave sorting endosomes after HEp2 cells were labeled to steady state with fluorescein Tf instead of the brief pulse used previously. We determined this rate using digital image analysis to measure the Tf content of sorting endosomes that also contained LDL. With an 11-min chase, the Tf in sorting endosomes was 24% of steady-state value. This was in excess of the amount expected (5% of steady state) from the rate of Tf exit after short filling pulses. The excess could not be accounted for by reinternalization of recycled cell surface Tf, implying that either some Tf was retained in sorting endosomes, or that Tf was delivered back to the sorting endosomes from the recycling compartment. The former is unlikely since nearly all sorting endosomes contain detectable Tf after an 11-min chase, even though more than one third of the sorting endosomes were formed during the chase time. Furthermore, while observing living cells by confocal microscopy, we saw vesicle movements that appeared to be fluorescent Tf returning from recycling compartments to sorting endosomes. The slow rate of exit after steady-state labeling was similar to the Tf exit rate from the cell, suggesting an equilibration of Tf throughout the early endosomal system by this retrograde pathway. This retrograde traffic may be important for delivering molecules from the recycling compartment, which is a long-lived organelle, to sorting endosomes, which are transient.


1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Salam Adel Al-Bayati ◽  
Luiz C. Wrobel

Purpose The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction. Design/methodology/approach The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence. Findings The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency. Originality/value Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.


Sign in / Sign up

Export Citation Format

Share Document