An isogeometric finite element formulation for phase transitions on deforming surfaces

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation. Both PDEs can be efficiently discretized using $C^1$-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise $C^1$-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-$\alpha$ scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to the text, added supplementary movie file

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$\alpha$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.Comment: In this version, typos were fixed, Fig. 16 is added, the literature review is extended and clarifying explanations and remarks are added at several places. Supplementary movies are available at https://av.tib.eu/series/641/supplemental+videos+of+the+paper+an+adaptive+space+time+phase+field+formulation+for+dynamic+fracture+of+brittle+shells+based+on+lr+nurb

Correction: International Society of Sports Nutrition position stand: Nutrient timing

Position Statement: The position of the Society regarding nutrient timing and the intake of carbohydrates, proteins, and fats in reference to healthy, exercising individuals is summarized by the following eight points: 1.) Maximal endogenous glycogen stores are best promoted by following a high-glycemic, high-carbohydrate (CHO) diet (600 – 1000 grams CHO or ~8 – 10 g CHO/kg/d), and ingestion of free amino acids and protein (PRO) alone or in combination with CHO before resistance exercise can maximally stimulate protein synthesis. 2.) During exercise, CHO should be consumed at a rate of 30 – 60 grams of CHO/hour in a 6 – 8% CHO solution (8 – 16 fluid ounces) every 10 – 15 minutes. Adding PRO to create a CHO:PRO ratio of 3 – 4:1 may increase endurance performance and maximally promotes glycogen re-synthesis during acute and subsequent bouts of endurance exercise. 3.) Ingesting CHO alone or in combination with PRO during resistance exercise increases muscle glycogen, offsets muscle damage, and facilitates greater training adaptations after either acute or prolonged periods of supplementation with resistance training. 4.) Post-exercise (within 30 minutes) consumption of CHO at high dosages (8 – 10 g CHO/kg/day) have been shown to stimulate muscle glycogen re-synthesis, while adding PRO (0.2 g – 0.5 g PRO/kg/day) to CHO at a ratio of 3 – 4:1 (CHO: PRO) may further enhance glycogen re-synthesis. 5.) Post-exercise ingestion (immediately to 3 h post) of amino acids, primarily essential amino acids, has been shown to stimulate robust increases in muscle protein synthesis, while the addition of CHO may stimulate even greater levels of protein synthesis. Additionally, pre-exercise consumption of a CHO + PRO supplement may result in peak levels of protein synthesis. 6.) During consistent, prolonged resistance training, post-exercise consumption of varying doses of CHO + PRO supplements in varying dosages have been shown to stimulate improvements in strength and body composition when compared to control or placebo conditions. 7.) The addition of creatine (Cr) (0.1 g Cr/kg/day) to a CHO + PRO supplement may facilitate even greater adaptations to resistance training. 8.) Nutrient timing incorporates the use of methodical planning and eating of whole foods, nutrients extracted from food, and other sources. The timing of the energy intake and the ratio of certain ingested macronutrients are likely the attributes which allow for enhanced recovery and tissue repair following high-volume exercise, augmented muscle protein synthesis, and improved mood states when compared with unplanned or traditional strategies of nutrient intake

Translational models for vascular cognitive impairment: a review including larger species.

BACKGROUND: Disease models are useful for prospective studies of pathology, identification of molecular and cellular mechanisms, pre-clinical testing of interventions, and validation of clinical biomarkers. Here, we review animal models relevant to vascular cognitive impairment (VCI). A synopsis of each model was initially presented by expert practitioners. Synopses were refined by the authors, and subsequently by the scientific committee of a recent conference (International Conference on Vascular Dementia 2015). Only peer-reviewed sources were cited. METHODS: We included models that mimic VCI-related brain lesions (white matter hypoperfusion injury, focal ischaemia, cerebral amyloid angiopathy) or reproduce VCI risk factors (old age, hypertension, hyperhomocysteinemia, high-salt/high-fat diet) or reproduce genetic causes of VCI (CADASIL-causing Notch3 mutations). CONCLUSIONS: We concluded that (1) translational models may reflect a VCI-relevant pathological process, while not fully replicating a human disease spectrum; (2) rodent models of VCI are limited by paucity of white matter; and (3) further translational models, and improved cognitive testing instruments, are required

A Renewable Tissue Resource of Phenotypically Stable, Biologically and Ethnically Diverse, Patient-Derived Human Breast Cancer Xenograft Models

Breast cancer research is hampered by difficulties in obtaining and studying primary human breast tissue, and by the lack of in vivo preclinical models that reflect patient tumor biology accurately. To overcome these limitations, we propagated a cohort of human breast tumors grown in the epithelium-free mammary fat pad of SCID/Beige and NOD/SCID/IL2γ-receptor null (NSG) mice, under a series of transplant conditions. Both models yielded stably transplantable xenografts at comparably high rates (~21% and ~19%, respectively). Of the conditions tested, xenograft take rate was highest in the presence of a low-dose estradiol pellet. Overall, 32 stably transplantable xenograft lines were established, representing 25 unique patients. Most tumors yielding xenografts were “triple-negative” (ER-PR-HER2+) (n=19). However, we established lines from three ER-PR-HER2+ tumors, one ER+PR-HER2−, one ER+PR+HER2− and one “triple-positive” (ER+PR+HER2+) tumor. Serially passaged xenografts show biological consistency with the tumor of origin, are phenotypically stable across multiple transplant generations at the histologic, transcriptomic, proteomic, and genomic levels, and show comparable treatment responses as those observed clinically. Xenografts representing 12 patients, including two ER+ lines, showed metastasis to the mouse lung. These models thus serve as a renewable, quality-controlled tissue resource for preclinical studies investigating treatment response and metastasis

In-Plane Complex Potentials for a Special Class of Materials with Degenerate Piezoelectric Properties

Abstract In this paper, complex potentials for the solution of two-dimensional, in-plane, linear piezoelectric boundary value problems are presented. These potentials are only valid for a special set of piezoelectric properties that have been identified as being useful in nonlinear ferroelectric constitutive laws. In contrast to more general solution procedures like the Stroh or Lekhnitskii formalisms, the complex potentials derived here are dependent on explicit, closed-form combinations of the piezoelectric material properties. Under either plane strain or plane stress conditions, three complex potentials are required to determine the full set of electrical and mechanical field quantities. The components of stress, strain, displacement, electric field, electric displacement, and electric potential will all be given in terms of these three potentials. To demonstrate the solution to a boundary value problem with these potentials, the asymptotic fields near a crack tip in these materials are presented in closed form

A Continuum Thermodynamics Formulation for Micro-MagnetoMechanics with Applications to Ferromagnetic Shape Memory Alloys

a b s t r a c t A continuum thermodynamics formulation for micromagnetics coupled with mechanics is devised to model the evolution of magnetic domain and martensite twin structures in ferromagnetic shape memory alloys. The theory falls into the class of phase-field or diffuseinterface modeling approaches. In addition to the standard mechanical and magnetic balance laws, two sets of micro-forces and their associated balance laws are postulated; one set for the magnetization order parameter and one set for the martensite order parameter. Next, the second law of thermodynamics is analyzed to identify the appropriate material constitutive relationships. The proposed formulation does not constrain the magnitude of the magnetization to be constant, allowing for spontaneous magnetization changes associated with strain and temperature. The equations governing the evolution of the magnetization are shown to reduce to the commonly accepted Landau-Lifshitz-Gilbert equations for the case where the magnetization magnitude is constant. Furthermore, the analysis demonstrates that under certain limiting conditions, the equations governing the evolution of the martensite-free strain are shown to be equivalent to a hyperelastic strain gradient theory. Finally, numerical solutions are presented to investigate the fundamental interactions between the magnetic domain wall and the martensite twin boundary in ferromagnetic shape memory alloys. These calculations determine under what conditions the magnetic domain wall and the martensite twin boundary can be dissociated, resulting in a limit to the actuating strength of the material

Salt-Induced Swelling and Volume Phase Transition of Polyelectrolyte Gels

A theoretical model of polyelectrolyte gels is presented to study continuous and discontinuous volume phase transitions induced by changing salt concentration in the external solution. Phase diagrams are constructed in terms of the polymer-solvent interaction parameters, external salt concentration, and concentration of fixed charges. Comparisons with previous experiments for an ionized acrylamide gel in mixed water-acetone solvents are made with good quantitative agreement for a monovalent salt (NaCl) but fair qualitative agreement for a divalent salt (MgCl 2 ), using a simple set of parameters for both cases. The effective polymer-solvent interactions vary with the volume fraction of acetone in the mixed solvent, leading to either continuous or discontinuous volume transitions. The presence of divalent ions (Mg 2þ ) in addition to monovalent ions in the external solution reduces the critical salt concentration for the discontinuous transition by several orders of magnitude. Moreover, a secondary continuous transition is predicted between two highly swollen states for the case of a divalent salt. The present model may be further extended to study volume phase transitions of polyelectrolyte gels in response to other stimuli such as temperature, pH and electrical field