scholarly journals Stability, free energy and dynamics of multi-spikes in the minimal Keller-Segel model

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanze Kong ◽  
Qi Wang
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Global Dynamics ◽  
Phase Transition Behavior ◽  
Chemotaxis Model ◽  
Numerical Studies ◽  
Long Time ◽  
The Stability ◽  
Single Boundary ◽  
Least Energy

<p style='text-indent:20px;'>One of the most impressive findings in chemotaxis is the aggregation that randomly distributed bacteria, when starved, release a diffusive chemical to attract and group with others to form one or several stable aggregates in a long time. This paper considers pattern formation within the minimal Keller–Segel chemotaxis model with a focus on the stability and dynamics of its multi-spike steady states. We first show that any steady-state must be a periodic replication of the spatially monotone one and they present multi-spikes when the chemotaxis rate is large; moreover, we prove that all the multi-spikes are unstable through their refined asymptotic profiles, and then find a fully-fledged hierarchy of free entropy energy of these aggregates. Our results also complement the literature by finding that when the chemotaxis is strong, the single boundary spike has the least energy hence is the most stable, the steady-state with more spikes has larger free energy, while the constant has the largest free energy and is always unstable. These results provide new insights into the model's intricate global dynamics, and they are illustrated and complemented by numerical studies which also demonstrate the metastability and phase transition behavior in chemotactic movement.</p>

QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS

2003 ◽  
Vol 13 (01) ◽  
pp. 19-33 ◽  
Author(s):  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Qualitative Analysis ◽  
Transition Probability ◽  
Steady State Solution ◽  
State Solution ◽  
Transition Probability Density ◽  
Capillary Formation ◽  
Long Time ◽  
The Stability

Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.

Sustainability and adaptability of regional development in the conditions of digitalization

2020 ◽  
Vol 19 (9) ◽  
pp. 1550-1613
Author(s):  
O.E. Akimova ◽  
S.K. Volkov ◽  
E.A. Gladkaya ◽  
I.M. Kuzlaeva
Keyword(s):  
Sustainable Development ◽  
Regional Development ◽  
Economic Behavior ◽  
Regional Inequality ◽  
Environmental Damage ◽  
Economic Potential ◽  
Human Welfare ◽  
Long Time ◽  
The Stability ◽  
Smart Technologies

Subject. The article discusses the sustainability of regional economy development, its definition, and the substance of sustainable development. Objectives. We aim at performing a comprehensive analysis of indicators of sustainability and adaptability of regional development in the context of digitalization, formulating a strategy for economic behavior that takes into account the multidimensional nature of regional inequality and is focused on boosting the economic potential of regions. Methods. The study draws on dialectic and systems approaches, general scientific methods of retrospective, situational, economic and statistical, and comparative analysis. Results. The sustainability of the region focuses on improving the human welfare over long time horizon. This happens in three areas, i.e. maximizing the efficiency of resource use; ensuring justice and democracy; minimizing resource consumption and environmental damage. The stability of the region can be assessed by using one parameter, or by combining the parameters in accordance with the type of region and expected results. Conclusions. The adaptation of a region to changing conditions depends on its type (‘adapted’, ‘adaptive’, and ‘non-adapted’). Regional inequality has two main components: difference in economic potential and social satisfaction of residents. Another component, affecting the stability and adaptability of regions, is the level of their digitalization. However, some regions have only formally embarked on the path of digitalization. Moreover, a focus on smart technologies, solutions and digitalization often leads to ignoring the goals of sustainable development. Smart technologies should be aimed at ensuring sustainability within the framework of the smart sustainable city concept.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

Effects of slide-to-roll ratio and varying velocity on the lubrication performance of grease at low speed

2021 ◽  
pp. 135065012199336
Author(s):  
Yiming Han ◽  
Jing Wang ◽  
Xuyang Jin ◽  
Shanshan Wang ◽  
Rui Zhang
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Industrial Applications ◽  
Transient Effects ◽  
Disintegration Time ◽  
Low Speed ◽  
Existence Time ◽  
Pure Rolling ◽  
Lubrication Performance ◽  
Long Time

Under steady-state pure rolling conditions with low speed, the thickener fiber agglomerations can be maintained for a long time, generating a beneficial thicker film thickness. However, in industrial applications, motions with sliding or transient effects are very common for gears, rolling-element bearings or even chain drives, evaluation of the grease performance under such conditions is vital for determining the lubrication mechanism and designing new greases. In this project, optical interferometry experiments were carried out on a ball-disk test rig to study the disintegration time of the grease thickener agglomerations with the increase of the slide-to-roll ratio under steady-state and reciprocation motions. Under steady-state conditions, the thickener fiber agglomeration can exist for a while and the time becomes shorter with the increase of the slide-to-roll ratio above the critical speed. Below the critical speed, the thickener fiber can exist in the contact in the form of a quite thick film for a very long time under pure rolling conditions but that time is decreased with the increase of the slide-to-roll ratio. The introduction of the transient effect can further reduce the existence time of the thickener.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Climate Change and Internet of Things Technologies—Sustainable Premises of Extending the Culture of the Amurg Cultivar in Transylvania—A Use Case for Târnave Vineyard

2021 ◽  
Vol 13 (15) ◽  
pp. 8170
Author(s):  
Veronica Sanda Chedea ◽  
Ana-Maria Drăgulinescu  ◽  
Liliana Lucia Tomoiagă  ◽  
Cristina Bălăceanu ◽  
Maria Lucia Iliescu 
Keyword(s):  
Climate Change ◽  
Weather Conditions ◽  
White Wine ◽  
Time Investment ◽  
Protected Designation Of Origin ◽  
Average Annual Temperature ◽  
Insect Infestations ◽  
Long Time ◽  
The Stability ◽  
Red Grape

Known for its dry and semi-dry white wine, the Târnave vineyard located in central Transylvania is challenged by the current climate change, which has resulted in an increase of the period of active vegetation by approximately 15–20 days, the average annual temperature by 1–1.5 °C and also the amount of useful temperatures (useful thermal balance for the grapevine). Furthermore, the frost periods have been reduced. Transylvania is an important Romanian region for grapevine cultivation. In this context, one can use the climatic changes to expand their wine assortment by cultivating an autochthonous grapevine variety called Amurg. Amurg is a red grape cultivar homologated at SCDVV Blaj, which also homologated 7 cultivars and 11 clones. Because viticulture depends on the stability of meteorological and hydrological parameters of the growing area, its foundations are challenged by climate change. Grapevine production is a long time investment, taking at least five years before the freshly planted vines produce the desired quality berries. We propose the implementation of a climate change-based precision viticulture turn-key solution for environmental monitoring in the Târnave vineyard. This solution aims to evaluate the grapevine’s micro-climate to extend the sustainable cultivation of the Amurg red grapes cultivar in Transylvania with the final goal of obtaining Protected Designation of Origin (PDO) rosé and red wines from this region. Worldwide, the changing conditions from the existing climate (a 30-year average), used in the past hundred years to dictate local standards, such as new and erratic trends of temperature and humidity regimes, late spring freezes, early fall frosts, storms, heatwaves, droughts, area wildfires, and insect infestations, would create dynamic problems for all farmers to thrive. These conditions will make it challenging to predict shifts in each of the components of seasonal weather conditions. Our proposed system also aims to give a solution that can be adapted to other vineyards as well.

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