On the convergence of a regularization scheme for approximating cavitation solutions with prescribed cavity volume size

Let $\Omega\in\mathbb{R}^n$, $n=2,3$, be the region occupied by a hyperelastic body in its reference configuration. Let $E(\cdot)$ be the stored energy functional, and let $x_0$ be a flaw point in $\Omega$ (i.e., a point of possible discontinuity for admissible deformations of the body). For V>0 fixed, let $u_V$ be a minimizer of $E(\cdot)$ among the set of discontinuous deformations $u$ constrained to form a hole of prescribed volume $V$ at $x_0$ and satisfying the homogeneous boundary data $u(x)=Ax$ for $x\in\partial \Omega$. In this paper we describe a regularization scheme for the computation of both $u_V$ and $E(u_V)$ and study its convergence properties. In particular, we show that as the regularization parameter goes to zero, (a subsequence) of the regularized constrained minimizers converge weakly in $W^{1,p}(\Omega\setminus{{\mathcal{B}}_{\delta}(x_0)})$ to a minimizer $u_{V}$ for any \delta>0. We obtain various sensitivity results for the dependence of the energies and Lagrange multipliers of the regularized constrained minimizers on the boundary data $A$ and on the volume parameter $V$. We show that both the regularized constrained minimizers and $u_V$ satisfy suitable weak versions of the corresponding Euler--Lagrange equations. In addition we describe the main features of a numerical scheme for approximating $u_V$ and $E(u_V)$ and give numerical examples for the case of a stored energy function of an elastic fluid and in the case of the incompressible limit

Infinite energy cavitating solutions: a variational approach

We study the phenomenon of cavitation for the displacement boundary value problem of radial, isotropic compressible elasticity for a class of stored energy functions of the form $W(F) + h(\det F)$, where $W$ grows like $||F||^n$, and $n$ is the space dimension. In this case it follows (from a result of Vodopyanov, Goldshtein and Reshetnyak) that discontinuous deformations must have infinite energy. After characterizing the rate at which this energy blows up, we introduce a modified energy functional which differs from the original by a null lagrangian, and for which cavitating energy minimizers with finite energy exist. In particular, the Euler--Lagrange equations for the modified energy functional are identical to those for the original problem except for the boundary condition at the inner cavity. This new boundary condition states that a certain modified radial Cauchy stress function has to vanish at the inner cavity. This condition corresponds to the radial Cauchy stress for the original functional diverging to $-\infty$ at the cavity surface. Many previously known variational results for finite energy cavitating solutions now follow for the modified functional, such as the existence of radial energy minimizers, satisfaction of the Euler-Lagrange equations for such minimizers, and the existence of a critical boundary displacement for cavitation. We also discuss a numerical scheme for computing these singular cavitating solutions using regular solutions for punctured balls. We show the convergence of this numerical scheme and give some numerical examples including one for the incompressible limit case. Our approach is motivated in part by the use of the renormalized energy for Ginzberg-Landau vortices.Comment: 23 pages, 4 figure

Controls on terrestrial carbon feedbacks by productivity versus turnover in the CMIP5 Earth System Models

PublishedJournal Article© Author(s) 2015. To better understand sources of uncertainty in projections of terrestrial carbon cycle feedbacks, we present an approach to separate the controls on modeled carbon changes. We separate carbon changes into four categories using a linearized, equilibrium approach: those arising from changed inputs (productivity-driven changes), and outputs (turnover-driven changes), of both the live and dead carbon pools. Using Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations for five models, we find that changes to the live pools are primarily explained by productivity-driven changes, with only one model showing large compensating changes to live carbon turnover times. For dead carbon pools, the situation is more complex as all models predict a large reduction in turnover times in response to increases in productivity. This response arises from the common representation of a broad spectrum of decomposition turnover times via a multi-pool approach, in which flux-weighted turnover times are faster than mass-weighted turnover times. This leads to a shift in the distribution of carbon among dead pools in response to changes in inputs, and therefore a transient but long-lived reduction in turnover times. Since this behavior, a reduction in inferred turnover times resulting from an increase in inputs, is superficially similar to priming processes, but occurring without the mechanisms responsible for priming, we call the phenomenon "false priming", and show that it masks much of the intrinsic changes to dead carbon turnover times as a result of changing climate. These patterns hold across the fully coupled, biogeochemically coupled, and radiatively coupled 1 % yr-1 increasing CO2 experiments. We disaggregate inter-model uncertainty in the globally integrated equilibrium carbon responses to initial turnover times, initial productivity, fractional changes in turnover, and fractional changes in productivity. For both the live and dead carbon pools, inter-model spread in carbon changes arising from initial conditions is dominated by model disagreement on turnover times, whereas inter-model spread in carbon changes from fractional changes to these terms is dominated by model disagreement on changes to productivity in response to both warming and CO2 fertilization. However, the lack of changing turnover time control on carbon responses, for both live and dead carbon pools, in response to the imposed forcings may arise from a common lack of process representation behind changing turnover times (e.g., allocation and mortality for live carbon; permafrost, microbial dynamics, and mineral stabilization for dead carbon), rather than a true estimate of the importance of these processes.This research was supported by the Director, Office of Science, Office of Biological and Environmental Research of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231 as part of their Regional and Global Climate Modeling Program. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups listed in Table 1 for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. CDJ was supported by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101)

The 3rd World Conference on Kisspeptin, â Kisspeptin 2017: Brain and Beyondâ : Unresolved questions, challenges and future directions for the field

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144298/1/jne12600-sup-0001-FigS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144298/2/jne12600-sup-0002-FigS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144298/3/jne12600_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144298/4/jne12600.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144298/5/jne12600-sup-0003-FigS3.pd

Social connections predict brain structure in a multidimensional free-ranging primate society

Reproduction and survival in most primate species reflects management of both competitive and cooperative relationships. Here, we investigated the links between neuroanatomy and sociality in free-ranging rhesus macaques. In adults, the number of social partners predicted the volume of the mid–superior temporal sulcus and ventral-dysgranular insula, implicated in social decision-making and empathy, respectively. We found no link between brain structure and other key social variables such as social status or indirect connectedness in adults, nor between maternal social networks or status and dependent infant brain structure. Our findings demonstrate that the size of specific brain structures varies with the number of direct affiliative social connections and suggest that this relationship may arise during development. These results reinforce proposed links between social network size, biological success, and the expansion of specific brain circuits

High proportion of cactus species threatened with extinction

This is the author accepted manuscript. The final version is available from Nature Publishing Group via the DOI in this record.Consejo Nacional de Ciencia y Tecnologí