Testing Predictions of Optimal Migration Theory in Migratory Bats

Optimal migration theory is a framework used to evaluate trade-offs associated with migratory strategies. Two strategies frequently considered by migration theory are time minimizing, whereby migration is completed as quickly as possible, and energy minimizing, whereby migration is completed as energetically efficiently as possible. Despite extensive literature dedicated to generating analytical predictions about these migratory strategies, identifying appropriate study systems to empirically test predictions is difficult. Theoretical predictions that compare migratory strategies are qualitative, and empirical tests require that both time-minimizers and energy-minimizers are present in the same population; spring migrating silver-haired (Lasionycteris noctivagans) and hoary bats (Lasiurus cinereus) provide such a system. As both species mate in the fall, spring-migrating males are thought to be energy-minimizers while females benefit from early arrival to summering grounds, and are thought to be time-minimizers. Thermoregulatory expression also varies between species during spring migration, as female silver-haired bats and males of both species use torpor while female hoary bats, which implant embryos earlier, are thought to avoid torpor use which would delay pregnancy. Based on optimal migration theory, we predicted that female silver-haired bats and hoary bats would have increased fuel loads relative to males and the difference between fuel loads of male and female hoary bats would be greater than the difference between male and female silver-haired bats. We also predicted that females of both species would have a greater stopover foraging proclivity and/or assimilate nutrients at a greater rate than males. We then empirically tested our predictions using quantitative magnetic resonance to measure fuel load, δ13C isotope breath signature analysis to assess foraging, and 13C–labeled glycine to provide an indicator of nutrient assimilation rate. Optimal migration theory predictions of fuel load were supported, but field observations did not support the predicted refueling mechanisms, and alternatively suggested a reliance on increased fuel loads via carry-over effects. This research is the first to validate a migration theory prediction in a system of both time and energy minimizers and uses novel methodological approaches to uncover underlying mechanisms of migratory stopover use.

Convergence of Energy Minimizers of a MEMS Model in the Reinforced Limit

Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends to zero. The proof relies on the identification of the $\Gamma $ Γ -limit of the energy in this limit.

Effect of Periodic Arrays of Defects on Lattice Energy Minimizers

We consider interaction energies $$E_f[L]$$ E f [ L ] between a point $$O\in {\mathbb {R}}^d$$ O ∈ R d , $$d\ge 2$$ d ≥ 2 , and a lattice L containing O, where the interaction potential f is assumed to be radially symmetric and decaying sufficiently fast at infinity. We investigate the conservation of optimality results for $$E_f$$ E f when integer sublattices kL are removed (periodic arrays of vacancies) or substituted (periodic arrays of substitutional defects). We consider separately the non-shifted ($$O\in k L$$ O ∈ k L ) and shifted ($$O\not \in k L$$ O ∉ k L ) cases and we derive several general conditions ensuring the (non-)optimality of a universal optimizer among lattices for the new energy including defects. Furthermore, in the case of inverse power laws and Lennard-Jones-type potentials, we give necessary and sufficient conditions on non-shifted periodic vacancies or substitutional defects for the conservation of minimality results at fixed density. Different examples of applications are presented, including optimality results for the Kagome lattice and energy comparisons of certain ionic-like structures.

A continuously perturbed Dirichlet energy with area-preserving stationary points that ‘buckle’ and occur in equal-energy pairs

We exhibit a family of convex functionals with infinitely many equal-energy $$C^1$$ C 1 stationary points that (i) occur in pairs $$v_{\pm }$$ v ± satisfying $$\det \nabla v_{\pm }=1$$ det ∇ v ± = 1 on the unit ball B in $${\mathbb {R}}^2$$ R 2 and (ii) obey the boundary condition $$v_{\pm }=\text {id}$$ v ± = id on $$ \partial B$$ ∂ B . When the parameter $$\epsilon $$ ϵ upon which the family of functionals depends exceeds $$\sqrt{2}$$ 2 , the stationary points appear to ‘buckle’ near the centre of B and their energies increase monotonically with the amount of buckling to which B is subjected. We also find Lagrange multipliers associated with the maps $$v_{\pm }(x)$$ v ± ( x ) and prove that they are proportional to $$(\epsilon -1/\epsilon )\ln |x|$$ ( ϵ - 1 / ϵ ) ln | x | as $$x \rightarrow 0$$ x → 0 in B. The lowest-energy pairs $$v_{\pm }$$ v ± are energy minimizers within the class of twist maps (see Taheri in Topol Methods Nonlinear Anal 33(1):179–204, 2009 or Sivaloganathan and Spector in Arch Ration Mech Anal 196:363–394, 2010), which, for each $$0\le r\le 1$$ 0 ≤ r ≤ 1 , take the circle $$\{x\in B: \ |x|=r\}$$ { x ∈ B : | x | = r } to itself; a fortiori, all $$v_{\pm }$$ v ± are stationary in the class of $$W^{1,2}(B;{\mathbb {R}}^2)$$ W 1 , 2 ( B ; R 2 ) maps w obeying $$w=\text {id}$$ w = id on $$\partial B$$ ∂ B and $$\det \nabla w=1$$ det ∇ w = 1 in B.

The Legendre–Hadamard condition in Cosserat elasticity theory

Summary The Legendre–Hadamard necessary condition for energy minimizers is derived in the framework of Cosserat elasticity theory.

Crystallization in the hexagonal lattice for ionic dimers

We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some reference distance between different atomic types and include repulsive terms for atoms of the same type, which are typical assumptions in models for ionic dimers. Our goal is to show a two-dimensional crystallization result. More precisely, we give conditions in order to prove that energy minimizers are connected subsets of the hexagonal lattice where the two atomic types are alternately arranged in the crystal lattice. We also provide explicit formulas for the ground-state energy. Finally, we characterize the net charge, i.e. the difference of the number of the two atomic types. Analyzing the deviation of configurations from the hexagonal Wulff shape, we prove that for ground states consisting of [Formula: see text] particles the net charge is at most of order [Formula: see text] where the scaling is sharp.