scholarly journals Redundancy principle for optimal random search in biology

2017 ◽  
Author(s):  
Z. Schuss ◽  
K. Basnayake ◽  
D. Holcman
Keyword(s):  
Brownian Particle ◽  
Random Search ◽  
First Passage Time ◽  
Diffusion Flux ◽  
Chemical Activation ◽  
Nonlinear Dependence ◽  
Forward Rate ◽  
Geometrical Parameters ◽  
Activation Time ◽  
The Mean

AbstractChemical activation rate is traditionally determined by the diffusion flux into an absorbing ball, as computed by Smoluchowski in 1916. Thus the rate is set by the mean first passage time (MFPT) of a Brownian particle to a small target. This paradigm is shifted in this manuscript to set the time scale of activation in cellular biology to the mean time of the first among many arrivals of particles at the activation site. This rate is very different from the MFPT and depends on different geometrical parameters. The shift calls for the reconsideration of physical modeling such as deterministic and stochastic chemical reactions based on the traditional forward rate, especially for fast activation processes occurring in living cells. Consequently, the biological activation time is not necessarily exponential. The new paradigm clarifies the role of population redundancy in accelerating search processes and in defining cellular-activation time scales. This is the case, for example, in cellular transduction or in the nonlinear dependence of fertilization rate on the number of spermatozoa. We conclude that statistics of the extreme set the new laws of biology, which can be very different from the physical laws derived for individuals.

Transient properties of a bistable kinetic model with quantum corrections

Open Physics ◽  
2006 ◽  
Vol 4 (2) ◽  
Author(s):  
Bao-quan Ai ◽  
Hua Zheng ◽  
Hui-zhang Xie ◽  
Liang-gang Liu
Keyword(s):  
Low Temperatures ◽  
Brownian Particle ◽  
First Passage Time ◽  
Quantum Effects ◽  
Passage Time ◽  
Bistable System ◽  
Original Position ◽  
Quantum Corrections ◽  
Mean First Passage Time ◽  
The Mean

AbstractThe transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.

ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS

2021 ◽  
pp. 1-22
Author(s):  
S. IYANIWURA ◽  
M. J. WARD
Keyword(s):  
Brownian Particle ◽  
First Passage Time ◽  
Hexagonal Lattice ◽  
Passage Time ◽  
Lattice Points ◽  
Bravais Lattice ◽  
Mean First Passage Time ◽  
First Passage ◽  
Spatially Periodic ◽  
The Mean

Abstract A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as “traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.

Asymptotic analysis for the mean first passage time in finite or spatially periodic 2D domains with a cluster of small traps

2021 ◽  
Vol 63 ◽  
pp. 1-22
Author(s):  
Sarafa Iyaniwura ◽  
Michael Ward
Keyword(s):  
Brownian Particle ◽  
First Passage Time ◽  
Hexagonal Lattice ◽  
Passage Time ◽  
Lattice Points ◽  
Bravais Lattice ◽  
Mean First Passage Time ◽  
First Passage ◽  
Spatially Periodic ◽  
The Mean

A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as "traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps. doi:10.1017/S1446181121000018

scholarly journals Singular perturbations in noisy dynamical systems

2018 ◽  
Vol 29 (4) ◽  
pp. 570-593 ◽  
Author(s):  
B. J. MATKOWSKY
Keyword(s):  
Stable Equilibrium ◽  
Initial Conditions ◽  
Brownian Particle ◽  
First Passage Time ◽  
Domain Of Attraction ◽  
Passage Time ◽  
Mathematical Arguments ◽  
Spurious Solutions ◽  
The Mean ◽  
Deterministic Dynamical System

Consider a deterministic dynamical system in a domain containing a stable equilibrium, e.g., a particle in a potential well. The particle, independent of initial conditions, eventually reaches the bottom of the well. If however, the particle is subjected to white noise, due, e.g., to collisions with a population of smaller, lighter particles comprising the medium through which the particle travels, a dramatic difference in the behaviour of the Brownian particle occurs. The particle will exit the well. The natural questions then are how long will it take for it to exit and from where on the boundary of the domain of attraction of the deterministic equilibrium (the rim of the well) will it exit. We compute the mean first passage time to the boundary and the mean probabilities of the exit positions. When the noise is small each quantity satisfies a singularly perturbed deterministic boundary value problem. We treat the problem by the method of matched asymptotic expansions (MAE) and generalizations thereof. MAE has been used successfully to solve problems in many applications. However, there exist problems for which MAE does not suffice. Among these are problems exhibiting boundary layer resonance, i.e., the problem of ‘spurious solutions’, which led some to conclude that this was ‘the failure of MAE’. We present a physical argument and four mathematical arguments to modify or augment MAE to make it successful. Finally, we discuss applications of the theory.

Study of the process of forming a hole for a thread at manufacturing a high nut

2020 ◽  
Vol 76 (8) ◽  
pp. 841-846
Author(s):  
I. G. Shubin ◽  
A. A. Kurkin
Keyword(s):  
Metal Flow ◽  
Nonlinear Dependence ◽  
Geometrical Parameters ◽  
Relative Height ◽  
Forming Process ◽  
Normal Height ◽  
Accuracy Class ◽  
Limit Values ◽  
Program Complex ◽  
Class B

During manufacturing nuts of increased height, a problem of obtaining correct cylindrical form of the hole for thread and overall geometrical parameters arises. To solve the problem it is necessary to know regularity of the blank forming process. Results of the study of a technological process of high hexahedral nuts forming presented. The nuts were M18 of 22 mm height, M16 of 19 mm height and M12 of normal height 10 mm according to GOST 5915–70, accuracy class B, steel grade 10 according to GOST 10702–78. The volumetric stamping was accomplished at the five-position automatic presses of АА1822 type. It was determined, that unevenness of the metal flow in the process of plastic deformation of blanks of increased height nuts was caused by different stress conditions by their sections. To simulate the mode of deformation, the program complex QForm-3D was chosen. The complex ensured to forecast with necessary accuracy the metal flow in a blank, as well as to define the deformation force and arising stress in the working instrument. The simulation showed the presence of regularity between preliminary formed buffle and deviation of dimensions and form of a blank wall after its finishing piercing, which can be expressed by a nonlinear dependence. The limit values of the relative height of the buffle С/D = 0.56–0.588 defined, exceeding which will result in rejection of the finished product. Accounting the limit values of the relative height of the buffle will enable to correct a mode of technological operations and technological instruments at stamping of high hexahedral nuts.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Computer Analysis of the Effect of Activation Temperature on the Microporous Structure Development of Activated Carbon Derived from Common Polypody

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2951
Author(s):  
Mirosław Kwiatkowski ◽  
Jarosław Serafin ◽  
Andy M. Booth ◽  
Beata Michalkiewicz
Keyword(s):  
Activated Carbon ◽  
Porous Structure ◽  
Computer Analysis ◽  
Density Functional ◽  
Activated Carbons ◽  
Chemical Activation ◽  
Geometrical Parameters ◽  
Activation Process ◽  
Microporous Structure ◽  
Activation Temperature

This paper presents the results of a computer analysis of the effect of activation process temperature on the development of the microporous structure of activated carbon derived from the leaves of common polypody (Polypodium vulgare) via chemical activation with phosphoric acid (H3PO4) at activation temperatures of 700, 800, and 900 °C. An unconventional approach to porous structure analysis, using the new numerical clustering-based adsorption analysis (LBET) method together with the implemented unique gas state equation, was used in this study. The LBET method is based on unique mathematical models that take into account, in addition to surface heterogeneity, the possibility of molecule clusters branching and the geometric and energy limitations of adsorbate cluster formation. It enabled us to determine a set of parameters comprehensively and reliably describing the porous structure of carbon material on the basis of the determined adsorption isotherm. Porous structure analyses using the LBET method were based on nitrogen (N2), carbon dioxide (CO2), and methane (CH4) adsorption isotherms determined for individual activated carbon. The analyses carried out showed the highest CO2 adsorption capacity for activated carbon obtained was at an activation temperature of 900 °C, a value only slightly higher than that obtained for activated carbon prepared at 700 °C, but the values of geometrical parameters determined for these activated carbons showed significant differences. The results of the analyses obtained with the LBET method were also compared with the results of iodine number analysis and the results obtained with the Brunauer–Emmett–Teller (BET), Dubinin–Radushkevich (DR), and quenched solid density functional theory (QSDFT) methods, demonstrating their complementarity.

The Sears problem for a lifting airfoil revisited - new results

1984 ◽  
Vol 141 ◽  
pp. 109-122 ◽  
Author(s):  
H. M. Atassi
Keyword(s):  
Small Angle ◽  
Potential Flow ◽  
Angle Of Attack ◽  
Nonlinear Dependence ◽  
Mean Flow ◽  
Linear Superposition ◽  
Flow Angle ◽  
Independent Components ◽  
The Mean ◽  
Gust Response

It is shown that for a thin airfoil with small camber and small angle of attack moving in a periodic gust pattern, the unsteady lift caused by the gust can be constructed by linear superposition to the Sears lift of three independent components accounting separately for the effects of airfoil thickness, airfoil camber and non-zero angle of attack to the mean flow. This is true in spite of the nonlinear dependence of the unsteady flow on the mean potential flow of the airfoil. Specific lift formulas are derived and analysed to assess the importance of mean flow angle of attack and airfoil camber on the gust response.

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