اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSurvival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments
41
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of small mutations is characterized by a Hamilton-Jacobi equation with constraint that describes the concentration of the population on some traits. This result was already established in Barles-Perthame 2008, Barles-Mirrahimi-Perthame 2009, Lorz-Mirrahimi-Perthame 2011 in a time-homogenous environment, when the asymptotic persistence of the population was ensured by assumptions on either the growth rate or the initial data. Here, we relax these assumptions to extend the study to situations where the population may go extinct at the limit. For that purpose, we provide conditions on the initial data for the asymptotic fate of the population. Finally, we show how this study for a time-homogenous environment allows to consider temporally piecewise constant environments.
قيم البحث
اقرأ أيضاً
In this article, we are interested in the analysis and simulation of solutions to an optimal control problem motivated by population dynamics issues. In order to control the spread of mosquito-borne arboviruses, the population replacement technique c
onsists in releasing into the environment mosquitoes infected with the Wolbachia bacterium, which greatly reduces the transmission of the virus to the humans. Spatial releases are then sought in such a way that the infected mosquito population invades the uninfected mosquito population. Assuming very high mosquito fecundity rates, we first introduce an asymptotic model on the proportion of infected mosquitoes and then an optimal control problem to determine the best spatial strategy to achieve these releases. We then analyze this problem, including the optimality of natural candidates and carry out first numerical simulations in one dimension of space to illustrate the relevance of our approach.
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the main results
developed over the last decade for the estimation of the division rate in growing and dividing populations in a steady environment. These methods combine tools borrowed from PDEs and stochastic processes, with a certain view that emerges from mathematical statistics. A focus on the application to the bacterial cell division cycle provides a concrete presentation, and may help the reader to identify major new challenges in the field.
The continuum robot has attracted more attention for its flexibility. Continuum robot kinematics models are the basis for further perception, planning, and control. The design and research of continuum robots are usually based on the assumption of pi
ecewise constant curvature (PCC). However, due to the influence of friction, etc., the actual motion of the continuum robot is approximate piecewise constant curvature (APCC). To address this, we present a kinematic equivalent model for continuum robots, i.e. APCC 2L-5R. Using classical rigid linkages to replace the original model in kinematic, the APCC 2L-5R model effectively reduces complexity and improves numerical stability. Furthermore, based on the model, the configuration self-estimation of the continuum robot is realized by monocular cameras installed at the end of each approximate constant curvature segment. The potential of APCC 2L-5R in perception, planning, and control of continuum robots remains to be explored.
A general force-perturbation-based criterion for solid instability is proposed, which can predict instability including crease without priori knowledge of instability configuration. The crease instability is analyzed in detail, we found that the occu
rrence of solid instability does not always correspond to the non-positive definiteness of global stiffness matrix. An element stiffness-based criterion based on material stiffness is proposed as a stronger criterion in order to fast determine the occurrence of instability. This criterion has been shown to degenerate into the criterion for judging instability of certain known phenomena, such as necking and shear band phenomena. Besides, instability in strongly anisotropic materials is also predicted by the element stiffness-based criterion.
In this paper we consider the problem of minimizing area subject to a volume constraint in a given convex set.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
