On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this to a sum over the residues of the extended power spectral density. For systems where the parametric forcing term is a rank one matrix, this leads to an enormous simplification.Comment: 16 page

On the length of chains of proper subgroups covering a topological group

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain <G_a : a of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and $(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a subset of G_a. In case of the group Sym(w) of all permutations of w with the topology inherited from w^w this improves upon earlier results of S. Thomas

A Logic for Non-Deterministic Parallel Abstract State Machines

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Logical Dreams

We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic

Sub-unit cell layer-by-layer growth of Fe3O4, MgO, and Sr2RuO4 thin films

The use of oxide materials in oxide electronics requires their controlled epitaxial growth. Recently, it was shown that Reflection High Energy Electron Diffraction (RHEED) allows to monitor the growth of oxide thin films even at high oxygen pressure. Here, we report the sub-unit cell molecular or block layer growth of the oxide materials Sr2RuO4, MgO, and magnetite using Pulsed Laser Deposition (PLD) from stoichiometric targets. Whereas for perovskites such as SrTiO3 or doped LaMnO3 a single RHEED intensity oscillation is found to correspond to the growth of a single unit cell, in materials where the unit cell is composed of several molecular layers or blocks with identical stoichiometry, a sub-unit cell molecular or block layer growth is established resulting in several RHEED intensity oscillations during the growth of a single unit-cell

Flow organization and heat transfer in turbulent wall sheared thermal convection

We perform direct numerical simulations of wall sheared Rayleigh-B\'enard (RB) convection for Rayleigh numbers up to $Ra=10^8$, Prandtl number unity, and wall shear Reynolds numbers up to $Re_w=10000$. Using the Monin-Obukhov length $L_{MO}$ we identify three different flow states, a buoyancy dominated regime ($L_{MO} \lesssim \lambda_{\theta}$; with $\lambda_{\theta}$ the thermal boundary layer thickness), a transitional regime ($0.5H \gtrsim L_{MO} \gtrsim \lambda_{\theta}$; with $H$ the height of the domain), and a shear dominated regime ($L_{MO} \gtrsim 0.5H$). In the buoyancy dominated regime the flow dynamics are similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed $Ra$ and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. For $L_{MO} \gtrsim 0.5H$ the Nusselt number $Nu$ effectively scales as $Nu \sim Ra^{\alpha}$, with $\alpha \ll 1/3$ while we find $\alpha \simeq 0.31$ in the buoyancy dominated regime. In the transitional regime the effective scaling exponent is $\alpha > 1/3$, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection

From nonlinear to linearized elasticity via Γ-convergence: the case of multiwell energies satisfying weak coercivity conditions

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled non- linear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers

The ultrafilter number for singular cardinals

We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.Comment: 8 page

Adding many Baumgartner clubs

I define a homogeneous ℵ2–c.c. proper product forcing for adding many clubs of ω1 with finite conditions. I use this forcing to build models of b(ω1)=ℵ2, together with d(ω1) and 2ℵ0 large and with very strong failures of club guessing at ω1