Probabilistic Response and Stochastic Bifurcation in a Turbulent Swirling Flow

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Xiaole Yue ◽  
Yanyan Wang ◽  
Qun Han ◽  
Yong Xu ◽  
Wei Xu
Keyword(s):  
Stochastic Dynamics ◽  
Swirling Flow ◽  
Gaussian Approximation ◽  
Stable State ◽  
Stochastic Bifurcation ◽  
Dimensional System ◽  
Stable States ◽  
Generalized Cell Mapping ◽  
Wide Range ◽  
Storage Problem

Abstract Stochastic dynamics in a turbulent swirling flow are reported in this paper via the probability density functions (PDFs) of responses with the generalized cell mapping (GCM) method. Based on the short-time Gaussian approximation (STGA) procedure, the influence generated by the time average and the amplitude of the fluctuation to the turbulent flow on the probabilistic responses are demonstrated. We observe that the shapes of the steady-state PDFs change from two peaks to the single peak with the change of system parameters, indicating that the rotation to shear ratio will change from two stable states into one stable state, while the torque difference of the propellers in the von-Karman turbulence experimental setup becomes large or changes in a wide range. That is to say, the stochastic P-bifurcation phenomena occur. The evolutionary mechanism of the transient response is revealed with the global portraits. Furthermore, the idea of block matrix is devoted to solving the storage problem due to the amount of image cells for the STGA procedure in high dimensional system. Monte Carlo (MC) simulations are in good agreement with the proposed strategy.

scholarly journals Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Julien Hurbain ◽  
Darka Labavić ◽  
Quentin Thommen ◽  
Benjamin Pfeuty
Keyword(s):  
Cell Fate ◽  
Stochastic Dynamics ◽  
Biochemical Networks ◽  
Stochastic Bifurcation ◽  
Modeling Framework ◽  
Life And Death ◽  
Cell Fate Decisions ◽  
Wide Range ◽  
Adaptation Response ◽  
The Impact

Abstract Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

scholarly journals Effect of Energy Degeneracy on the Transition Time for a Series of Metastable States

2021 ◽  
Vol 184 (1) ◽  
Author(s):  
Gianmarco Bet ◽  
Vanessa Jacquier ◽  
Francesca R. Nardi
Keyword(s):  
Metastable State ◽  
Stochastic Dynamics ◽  
Transition Probabilities ◽  
Mixing Time ◽  
Stable State ◽  
Temperature Limit ◽  
Metastable States ◽  
Transition Time ◽  
Sharp Estimates ◽  
Model Independent

AbstractWe consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in several directions. First, we give an estimate of the mixing time of the dynamics in terms of the maximal stability level. Second, assuming the dynamics is reversible, we give an estimate of the associated spectral gap. Third, we give precise asymptotics for the expected transition time from any metastable state to the stable state using potential-theoretic techniques. We do this in a general reversible setting where two or more metastable states are allowed and some of them may even be degenerate. This generalizes previous results that hold for a series of only two metastable states. We then focus on a specific Probabilistic Cellular Automata (PCA) with configuration space $${\mathcal {X}}=\{-1,+1\}^\varLambda $$ X = { - 1 , + 1 } Λ where $$\varLambda \subset {\mathbb {Z}}^2$$ Λ ⊂ Z 2 is a finite box with periodic boundary conditions. We apply our model-independent results to find sharp estimates for the expected transition time from any metastable state in $$\{\underline{-1}, {\underline{c}}^o,{\underline{c}}^e\}$$ { - 1 ̲ , c ̲ o , c ̲ e } to the stable state $$\underline{+1}$$ + 1 ̲ . Here $${\underline{c}}^o,{\underline{c}}^e$$ c ̲ o , c ̲ e denote the odd and the even chessboard respectively. To do this, we identify rigorously the metastable states by giving explicit upper bounds on the stability level of every other configuration. We rely on these estimates to prove a recurrence property of the dynamics, which is a cornerstone of the pathwise approach to metastability.

Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hao Dong ◽  
Lin Du ◽  
Rongchun Hu ◽  
Shuo Zhang ◽  
Zichen Deng
Keyword(s):  
High Efficiency ◽  
Stochastic Dynamics ◽  
Stretch Ratio ◽  
Dielectric Elastomer ◽  
Mapping Method ◽  
The State ◽  
Stochastic Dynamic ◽  
Steady State Probability ◽  
Generalized Cell Mapping ◽  
Biological Compatibility

Abstract Dielectric elastomers are widely used in many fields due to their advantages of high deformability, light weight, biological compatibility, and high efficiency. In this study, the stochastic dynamic response and bifurcation of a dielectric elastomer balloon (DEB) with viscoelasticity are investigated. Firstly, the rheological model is adopted to describe the viscoelasticity of the DEB, and the dynamic model is deduced by using the free energy method. The effect of viscoelasticity on the state of equilibrium with static pressure and voltage is analysed. Then, the stochastic differential equation about the perturbation around the state of equilibrium is derived when the DEB is under random pressure and static voltage. The steady-state probability densities of the perturbation stretch ratio are determined by the generalized cell mapping method. The effects of parameter conditions on the mean value of the perturbation stretch ratio are calculated. Finally, sinusoidal voltage and random pressure are applied to the viscoelastic DEB, and the phenomenon of P-bifurcation is observed. Our results are compared with those obtained from Monte Carlo simulation to verify their accuracy. This work provides a potential theoretical reference for the design and application of DEs.

scholarly journals Path-dependent institutions drive alternative stable states in conservation

2018 ◽  
Vol 116 (2) ◽  
pp. 689-694 ◽  
Author(s):  
Edward W. Tekwa ◽  
Eli P. Fenichel ◽  
Simon A. Levin ◽  
Malin L. Pinsky
Keyword(s):  
Renewable Resources ◽  
Path Dependence ◽  
Alternative Stable States ◽  
Stable State ◽  
Empirical Support ◽  
Stable States ◽  
Alternative Stable State ◽  
Important Challenge ◽  
Quantitative Analyses ◽  
Path Dependent

Understanding why some renewable resources are overharvested while others are conserved remains an important challenge. Most explanations focus on institutional or ecological differences among resources. Here, we provide theoretical and empirical evidence that conservation and overharvest can be alternative stable states within the same exclusive-resource management system because of path-dependent processes, including slow institutional adaptation. Surprisingly, this theory predicts that the alternative states of strong conservation or overharvest are most likely for resources that were previously thought to be easily conserved under optimal management or even open access. Quantitative analyses of harvest rates from 217 intensely managed fisheries supports the predictions. Fisheries’ harvest rates also showed transient dynamics characteristic of path dependence, as well as convergence to the alternative stable state after unexpected transitions. This statistical evidence for path dependence differs from previous empirical support that was based largely on case studies, experiments, and distributional analyses. Alternative stable states in conservation appear likely outcomes for many cooperatively managed renewable resources, which implies that achieving conservation outcomes hinges on harnessing existing policy tools to navigate transitions.

Inner-product theory calculations for some rational potentials in a three-dimensional system

1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Inner Product ◽  
Dimensional System ◽  
Product Technique ◽  
Special Cases ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Three Dimensional System ◽  
Range Of Values

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.

scholarly journals Influence of pipeline geometry on hydrodynamics and heat transfer processes by an example of a ship steam generator

2021 ◽  
Vol 2088 (1) ◽  
pp. 012033
Author(s):  
O V Mitrofanova ◽  
A V Fedorinov
Keyword(s):  
Nuclear Power ◽  
Large Scale ◽  
Complex Geometry ◽  
Swirling Flow ◽  
Thermal Power ◽  
Design Parameters ◽  
Nuclear Power Installation ◽  
Wide Range ◽  
Nuclear Power Installations ◽  
Power Installations

Abstract The theoretical and computational analysis proposed in this work is aimed at identifying the features of thermal and hydrodynamic processes carried out in the steam-generating channels of the ship type water-moderated nuclear power installations. It is shown that the complex geometry of the thermohydraulic tract curvilinear channels of the steam generating system has a significant effect on the efficiency of the transport nuclear power installation. In addition to the formation of large-scale vortex structures and swirling flow in the pipeline, the phenomenon of the swirling flow crisis is revealed, under which the low-frequency component of the acoustic spectrum is enhanced. The scientific and applied significance of the proposed research is associated with the need to ensure a wide range of operational changes in efficient and safe operation power modes of icebreaker nuclear power installations. The research, aimed at developing the principles of physical and mathematical modeling of complex vortex flows, is necessary to optimize the design parameters of the thermal power equipment elements of new generation ship nuclear power installations in order to ensure increased safety and reliability of their operation.

scholarly journals Stability analysis of a signaling circuit with dual species of GTPase switches

2020 ◽  
Author(s):  
Lucas Martins Stolerman ◽  
Pradipta Ghosh ◽  
Padmini Rangamani
Keyword(s):  
Stability Analysis ◽  
Feedback Loop ◽  
Network Motif ◽  
Bound State ◽  
Steady States ◽  
Eukaryotic Cells ◽  
Nucleotide Exchange ◽  
Organelle Biogenesis ◽  
Stable States ◽  
Wide Range

GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, and function, vesicular transport between organelles, and signal transduction. These hydrolase enzymes operate by toggling between an active "ON") guanosine triphosphate (GTP)-bound state and an inactive ("OFF") guanosine diphosphate (GDP)-bound state; such a toggle is regulated by GEFs (guanine nucleotide exchange factors) and GAPs (GTPase activating proteins). Here we propose a model for a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. We develop a system of ordinary differential equations in which these two classes of GTPases are interlinked conditional to their ON/OFF states within a motif through coupling and feedback loops. We provide explicit formulae for the steady states of the system and perform classical local stability analysis to systematically investigate the role of the different connections between the GTPase switches. Interestingly, a coupling of the active mGTPase to the GEF of the tGTPase was sufficient to provide two locally stable states: one where both active/inactive forms of the mGTPase can be interpreted as having low concentrations and the other where both m- and tGTPase have high concentrations. Moreover, when a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the coupled system, two other locally stable states emerged, both having the tGTPase inactivated and being interpreted as having low active tGTPase concentrations. Finally, the addition of a second feedback loop, from the active tGTPase to the GAP of the mGTPase, gives rise to a family of steady states that can be parametrized by a range of inactive tGTPase concentrations. Our findings reveal that the coupling of these two different GTPase motifs can dramatically change their steady state behaviors and shed light on how such coupling may impact signaling mechanisms in eukaryotic cells.

scholarly journals Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

2021 ◽  
Vol 9 ◽  
Author(s):  
A. R. Ramos Ramos ◽  
O. Kühn
Keyword(s):  
Optimal Control ◽  
Gaussian Approximation ◽  
Gaussian Function ◽  
Dynamical Equations ◽  
Control Approach ◽  
Wide Range ◽  
Bistable Potential ◽  
Wavepacket Dynamics ◽  
Direct Optimal Control ◽  
Backward Propagation

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

Design and Characterization of Single Beam for Latching Electrothermal Microswitch

2012 ◽  
Vol 468-471 ◽  
pp. 286-289
Author(s):  
Ying Zhang ◽  
Hong Wang ◽  
Yan Wang ◽  
Sheng Ping Mao ◽  
Gui Fu Ding
Keyword(s):  
Mechanical Performance ◽  
Stable State ◽  
Cantilever Beams ◽  
Analysis Software ◽  
Stable States ◽  
Element Analysis ◽  
Single Beam ◽  
Fabrication And Characterization ◽  
Continuous Power

This paper presents the design, fabrication and characterization of single beam for latching electrothermal microswitch. This microswitch consists of two cantilever beams using bimorph electrothermal actuator with mechanical latching for performing low power bistable relay applications. A stable state can be acquired without continuous power which is only needed to switch between two stable states of the microactuator. The single beam is discussed mainly to judge the possibility of realizing the designed function. First, reasonable shape of the resistance is designed using finite element analysis software ANSYS. Then, mechanical performance was characterized by WYKO NT1100 optical profiling system, the tip deflection of single beam can meet the designed demand.

scholarly journals Manipulation of the swirling flow instability in hydraulic turbine diffuser by different methods of water injection

2018 ◽  
Vol 180 ◽  
pp. 02090 ◽  
Author(s):  
Pavel Rudolf ◽  
Jiří Litera ◽  
Germán Alejandro Ibarra Bolanos ◽  
David Štefan
Keyword(s):  
Swirling Flow ◽  
Flow Instability ◽  
Draft Tube ◽  
Water Injection ◽  
Hydraulic Turbine ◽  
Operating Conditions ◽  
Francis Turbine ◽  
Necessary Condition ◽  
Vortex Rope ◽  
Wide Range

Vortex rope, which induces substantial pressure pulsations, arises in the draft tube (diffuser) of Francis turbine for off-design operating conditions. Present paper focuses on mitigation of those pulsations using active water jet injection control. Several modifications of the original Susan-Resiga’s idea were proposed. All modifications are driven by manipulation of the shear layer region, which is believed to play important role in swirling flow instability. While some of the methods provide results close to the original one, none of them works in such a wide range. Series of numerical experiments support the idea that the necessary condition for vortex rope pulsation mitigation is increasing the fluid momentum along the draft tube axis.

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