Radiator design system computer programs

Minimum weight space radiator subsystems which can operate over heat load ranges wider than the capabilities of current subsystems are investigated according to projected trends of future long duration space vehicles. Special consideration is given to maximum heat rejection requirements of the low temperature radiators needed for environmental control systems. The set of radiator design programs that have resulted from this investigation are presented in order to provide the analyst with a capability to generate optimum weight radiator panels or sets of panels from practical design considerations, including transient performance. Modifications are also provided for existing programs to improve capability and user convenience

A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Dynamical epidemic suppression using stochastic prediction and control

We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control. scheme that prevents large outbreaks from occurring. The theory inapplicable to a wide range of stochastic processes with underlying deterministic structure.Comment: 14 pages, 6 figure

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Internal displacement reactions in multicomponent oxides. Part I. Line compounds with narrow homogeneity range

As a model of an internal displacement reaction involving a ternary oxide "line" compound, the following reaction was studied at 1273 K as a function of time, t: Fe + NiTiO3 = "Ni" + "FeTiO3" Both polycrystalline and single-crystal materials were used as the starting NiTiO3 oxide. During the reaction, the Ni in the oxide compound is displaced by Fe and it precipitates as a γ-(Ni-Fe) alloy. The reaction preserves the starting ilmenite structure. The product oxide has a constant Ti concentration across the reaction zone, with variation in the concentration of Fe and Ni, consistent with ilmenite composition. In the case of single-crystal NiTiO3 as the starting oxide, the γ alloy has a "layered" structure and the layer separation is suggestive of Liesegang-type precipitation. In the case of polycrystalline NiTiO3 as the starting oxide, the alloy precipitates mainly along grain boundaries, with some particles inside the grains. A concentration gradient exists in the alloy across the reaction zone and the composition is >95 at. pct Ni at the reaction front. The parabolic rate constant for the reaction is kp = 1.3 × 10-12 m2 s-1 and is nearly the same for both single-crystal and polycrystalline oxides

Internal displacement reactions in multicomponent oxides: Part II. Oxide solid solutions of wide composition range

As models of internal displacement reactions in oxide solid solutions, the following reactions were studied at 1273 K as a function of time: Fe + NixMg1-x)O = Ni + (FexMg1-x)O Fe + (Co0.5Mg0.5)O = Co + (Fe0.5Mg0.5)O In both reactions, Ni or Co in the starting oxide is displaced by Fe and the γ-(Ni-Fe) or (Co-Fe) alloy is precipitated. In the reaction zone, composition gradients develop in both product phases, viz., the oxide and the alloy precipitate. The Ni (or Co) concentration of the alloy precipitate increases towards the reaction front. In the product oxide, the "inert" Mg diffuses toward the reaction front along with the Fe, while the Ni (or Co) diffusion is in the opposite direction, towards the Fe/boundary. The shape of the composition profiles for Mg and Fe in the product oxide suggests that cross-coefficient terms in the generalized flux equations contribute significantly to the cation flux. The parabolic rate constants of reactions involving Fe/(NixMg1-x)O decrease by nearly four orders of magnitude when x decreases from 1 to 0.1

A generalized theory of semiflexible polymers

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by the Renormalization Group. In particular, we show that either the WLC or our new model adequate describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors observed by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments

The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.Comment: 22 pages, 23 figures. Accepted for publication on Phys. Rev.

Twirling Elastica: Kinks, Viscous Drag, and Torsional Stress

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.Comment: 4 pages, 4 figure