Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Hastings-Levitov aggregation in the small-particle limit

We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web

Fantastic plastic? Experimental evaluation of polyurethane bone substitutes as proxies for human bone in trauma simulations

Recent years have seen steady improvements in the recognition and interpretation of violence related injuries in human skeletal remains. Such work has at times benefited from the involvement of biological anthropologists in forensic casework and has often relied upon comparison of documented examples with trauma observed in skeletal remains. In cases where no such example exists investigators must turn to experimentation. The selection of experimental samples is problematic as animal proxies may be too dissimilar to humans and human cadavers may be undesirable for a raft of reasons. The current article examines a third alternative in the form of polyurethane plates and spheres marketed as viable proxies for human bone in ballistic experiments. Through subjecting these samples to a range of impacts from both modern and archaic missile weapons it was established that such material generally responds similarly to bone on a broad, macroscopic scale but when examined in closer detail exhibits a range of dissimilarities that call for caution in extrapolating such results to real bone

Approaches for advancing scientific understanding of macrosystems

The emergence of macrosystems ecology (MSE), which focuses on regional- to continental-scale ecological patterns and processes, builds upon a history of long-term and broad-scale studies in ecology. Scientists face the difficulty of integrating the many elements that make up macrosystems, which consist of hierarchical processes at interacting spatial and temporal scales. Researchers must also identify the most relevant scales and variables to be considered, the required data resources, and the appropriate study design to provide the proper inferences. The large volumes of multi-thematic data often associated with macrosystem studies typically require validation, standardization, and assimilation. Finally, analytical approaches need to describe how cross-scale and hierarchical dynamics and interactions relate to macroscale phenomena. Here, we elaborate on some key methodological challenges of MSE research and discuss existing and novel approaches to meet them

DNA Product Formation in Female Sprague–Dawley Rats Following Polyhalogenated Aromatic Hydrocarbon (PHAH) Exposure

DNA oxidation damage has been regarded as one of the possible mechanisms for the hepatic carcinogenesis of dioxin-like compounds (DLCs). In this study, we evaluated the toxic equivalency factor (TEF) from the standpoint of induced DNA oxidation products and their relationship to toxicity and carcinogenicity. Nine DNA oxidation products were analyzed in the liver of female Sprague-Dawley rats exposed to 2,3,7,8-tetrachlorodibenzo-pdioxin (TCDD) alone or the tertiary mixture of TCDD, 3,3',4,4',5-pentachlorobiphenyl (PCB 126), and 2,3,4,7,8-pentachlorodibenzofuran (PeCDF) by gavage for 14, 31, and 53 weeks (5 days/week) by LC-MS/MS: 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxo-dGuo); 1,N6-etheno-2'-deoxyadenosine (1,N6-εdAdo); N2,3-ethenoguanine (N2,3-εG); 7-(2-oxoethly)guanine (7-OEG); 1,N2-etheno-2'-deoxyguanosine (1,N2-εdGuo); malondialdehyde (M1dGuo); acrolein (AcrdGuo); crotonaldehyde (CrdGuo); and 4-hydroxynonenal (HNEdGuo) derived 2'-deoxyguanosine adducts. Exposure to TCDD (100 ng/kg/day) significantly induced 1,N6-εdAdo at 31 and 53 weeks, while no increase of 8-oxo-dGuo was observed. Significant increases were observed for 8-oxo-dGuo and 1,N6-εdAdo at all time points following exposure to the tertiary mixture (TEQ 100 ng/kg/day). Exposure to TCDD for 53 weeks only significantly increased 1,N6-εdAdo, while increases of N2,3-εG and 7-OEG were only found in the highest dose group (100 ng/kg/day). Exposure to the tertiary mixture for 53 weeks had no effect on N2,3-εG in any exposure group (TEQ 0, 22, 46, or 100 ng/kg/day), while significant increases were observed for 1,N6-εdAdo (all dose groups), 8-oxo-dGuo (46 and 100 ng/kg/day), and 7-OEG (100 ng/kg/day). While no significant increase was observed at 53 weeks for 1,N2-εdGuo, M1dGuo, AcrdGuo, or CrdGuo following exposure to TCDD (100 ng/kg/day), all of them were significantly induced in animals exposed to the tertiary mixture (TEQ 100 ng/kg/day). This oxidation DNA product data suggest that the simple TEF methodology cannot be applied to evaluate the diverse patterns of toxic effects induced by DLCs

Metamorphosis of plasma turbulence-shear flow dynamics through a transcritical bifurcation

The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive.Comment: 17 pages, revtex text, 9 figures comprised of 16 postscript files. Submitted to Phys. Rev.

Unrelated Donor Allogeneic Hematopoietic Stem Cell Transplantation for Patients with Hemoglobinopathies Using a Reduced-Intensity Conditioning Regimen and Third-Party Mesenchymal Stromal Cells

AbstractAllogeneic hematopoietic stem cell transplantation for patients with a hemoglobinopathy can be curative but is limited by donor availability. Although positive results are frequently observed in those with an HLA-matched sibling donor, use of unrelated donors has been complicated by poor engraftment, excessive regimen-related toxicity, and graft-versus-host disease (GVHD). As a potential strategy to address these obstacles, a pilot study was designed that incorporated both a reduced-intensity conditioning and mesenchymal stromal cells (MSCs). Six patients were enrolled, including 4 with high-risk sickle cell disease (SCD) and 2 with transfusion-dependent thalassemia major. Conditioning consisted of fludarabine (150 mg/m2), melphalan (140 mg/m2), and alemtuzumab (60 mg for patients weighing > 30 kg and .9 mg/kg for patients weighing <30 kg). Two patients received HLA 7/8 allele matched bone marrow and 4 received 4-5/6 HLA matched umbilical cord blood as the source of HSCs. MSCs were of bone marrow origin and derived from a parent in 1 patient and from an unrelated third-party donor in the remaining 5 patients. GVHD prophylaxis consisted of cyclosporine A and mycophenolate mofetil. One patient had neutropenic graft failure, 2 had autologous hematopoietic recovery, and 3 had hematopoietic recovery with complete chimerism. The 2 SCD patients with autologous hematopoietic recovery are alive. The remaining 4 died either from opportunistic infection, GVHD, or intracranial hemorrhage. Although no infusion-related toxicity was seen, the cotransplantation of MSCs was not sufficient for reliable engraftment in patients with advanced hemoglobinopathy. Although poor engraftment has been observed in nearly all such trials to date in this patient population, there was no evidence to suggest that MSCs had any positive impact on engraftment. Because of the lack of improved engraftment and unacceptably high transplant-related mortality, the study was prematurely terminated. Further investigations into understanding the mechanisms of graft resistance and development of strategies to overcome this barrier are needed to move this field forward

Elucidating the long-range charge carrier mobility in metal halide perovskite thin films

Many optoelectronic properties have been reported for lead halide perovskite polycrystalline films. However, ambiguities in the evaluation of these properties remain, especially for long-range lateral charge transport, where ionic conduction can complicate interpretation of data. Here we demonstrate a new technique to measure the long-range charge carrier mobility in such materials. We combine quasi-steady-state photo-conductivity measurements (electrical probe) with photo-induced transmission and reflection measurements (optical probe) to simultaneously evaluate the conductivity and charge carrier density. With this knowledge we determine the lateral mobility to be ~ 2 cm2/Vs for CH3NH3PbI3 (MAPbI3) polycrystalline perovskite films prepared from the acetonitrile/methylamine solvent system. Furthermore, we present significant differences in long-range charge carrier mobilities, from 2.2 to 0.2 cm2/Vs, between films of contemporary perovskite compositions prepared via different fabrication processes, including solution and vapour phase deposition techniques. Arguably, our work provides the first accurate evaluation of the long-range lateral charge carrier mobility in lead halide perovskite films, with charge carrier density in the range typically achieved under photovoltaic operation

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Mechanical Properties of End-crosslinked Entangled Polymer Networks using Sliplink Brownian Dynamics Simulations

The mechanical properties of a polymeric network containing both crosslinks and sliplinks (entanglements) are studied using a multi-chain Brownian dynamics simulation. We coarse-grain at the level of chain segments connecting consecutive nodes (cross- or sliplinks), with particular attention to the Gaussian statistics of the network. Affine displacement of nodes is not imposed: their displacement as well as sliding of monomers through sliplinks is governed by force balances. The simulation results of stress in uniaxial extension and the full stress tensor in simple shear including the (non-zero) second normal stress difference are presented for monodisperse chains with up to 18 entanglements between two crosslinks. The cases of two different force laws of the subchains (Gaussian chains and chains with finite extensibility) for two different numbers of monomers in a subchain (no = 50 and no = 100) are examined. It is shown that the additivity assumption of slip- and crosslink contribution holds for sufficiently long chains with two or more entanglements, and that it can be used to construct the strain response of a network of infinitely long chains. An important consequence is that the contribution of sliplinks to the small-strain shear modulus is about &#8532; of the contribution of a crosslink