Uniform Contraction Research Articles

Equilibrium states for hyperbolic potentials

We prove the existence of finitely many ergodic equilibrium states for local homeomorphisms and hyperbolic potentials. We also deal with partially hyperbolic skew-products over non-uniformly expanding maps with uniform contraction on the fibre. For these systems we prove the existence and finiteness of the equilibrium states associated with a class of Hölder continuous potentials.

Effects of Fibroin Microcarriers on Inflammation and Regeneration of Deep Skin Wounds in Mice.

The process of tissue regeneration following damage takes place with direct participation of the immune system. The use of biomaterials as scaffolds to facilitate healing of skin wounds is a new and interesting area of regenerative medicine and biomedical research. In many ways, the regenerative potential of biological material is related to its ability to modulate the inflammatory response. At the same time, all foreign materials, once implanted into a living tissue, to varying degree cause an immune reaction. The modern approach to the development of bioengineered structures for applications in regenerative medicine should be directed toward using the properties of the inflammatory response that improve healing, but do not lead to negative chronic manifestations. In this work, we studied the effect of microcarriers comprised of either fibroin or fibroin supplemented with gelatin on the dynamics of the healing, as well as inflammation, during regeneration of deep skin wounds in mice. We found that subcutaneous administration of microcarriers to the wound area resulted in uniform contraction of the wounds in mice in our experimental model, and microcarrier particles induced the infiltration of immune cells. This was associated with increased expression of proinflammatory cytokines TNF, IL-6, IL-1β, and chemokines CXCL1 and CXCL2, which contributed to full functional recovery of the injured area and the absence of fibrosis as compared to the control group.

A numerical study of turbulence under temporally evolving axisymmetric contraction and subsequent relaxation

Direct numerical simulations using up to $4096^{3}$ grid points on a deforming domain have been used to study the response of initially isotropic turbulence to a period of spatially uniform axisymmetric contraction (with one extensional and two equally compressive directions) and subsequent relaxation. A time-dependent strain rate is formulated to closely correspond to the downstream evolution in the wind tunnel experiments of Ayyalasomayajula & Warhaft (J. Fluid Mech., vol. 566, 2006, pp. 273–307), with a smoothly varying 4 : 1 contraction ratio. The application of strain leads to anisotropy in both the large scales and the small scales, in a manner where nonlinear effects not considered in rapid-distortion theory play an important role. Upon termination of strain, the small scales quickly return to isotropy while a residual level of anisotropy appears to persist at the large scales. The simulations are shown to reproduce many key findings from experiments, including distinctive changes in the form of the one-dimensional spectra in the extensional direction that arise at sufficiently high Reynolds number, during both the straining and relaxation periods. Scale-dependent measures of anisotropy are presented in terms of one-dimensional spectra and axisymmetric versions of the energy spectrum. To explain the observed changes in spectral shapes, various terms in the spectral evolution equation representing rapid pressure strain, slow pressure strain, production, nonlinear transfer and viscous dissipation are computed, showing that nonlinear effects take a dominant role when a wide range of scales exists. In particular, the ‘double-peak’ spectral form observed in experiments at high Reynolds number is found to be a consequence of the small scales relaxing towards isotropy much faster than the large scales. A comparison of results obtained from computational domains of varying sizes and grid resolutions show that the numerical findings are robust.

Volume hyperbolicity and wildness

It is known that volume hyperbolicity (partial hyperbolicity and uniform expansion or contraction of the volume in the extremal bundles) is a necessary condition for robust transitivity or robust chain recurrence and hence for tameness. In this paper, on any $3$-manifold we build examples of quasi-attractors which are volume hyperbolic and wild at the same time. As a main corollary, we see that, for any closed $3$-manifold $M$, the space $\text{Diff}^{1}(M)$ admits a non-empty open set where every $C^{1}$-generic diffeomorphism has no attractors or repellers. The main tool of our construction is the notion of flexible periodic points introduced in the authors’ previous paper. In order to eject the flexible points from the quasi-attractor, we control the topology of the quasi-attractor using the notion of partially hyperbolic filtrating Markov partitions, which we introduce in this paper.

Stone Stability under Stationary Nonuniform Flows

AbstractA stability parameter for rock in bed protections under nonuniform stationary flow is derived. The influence of the mean flow velocity, turbulence, and mean acceleration of the flow are included explicitly in the parameter. The relatively new notion of explicitly incorporating the mean acceleration of the flow significantly improves the description of stone stability. The new stability parameter can be used in the design of granular bed protections using a numerical model for a large variety of flows. The coefficients in the stability parameter are determined by regarding the measured low-mobility entrainment rate of rock as a function of the stability parameter. Measurements of flow characteristics and stone entrainment of four different previous studies and many configurations (uniform flow, expansion, contraction, and sill) are used. These configurations have different relative contributions of mean flow, turbulence, and stationary acceleration. The coefficients in the parameter are fit to all ...

Mesomechanical model and analysis of an artificial muscle functioning: role of Poisson’s ratio

The mechanism of force generation in a polymer monofilament actuator element with auxetic characteristics is modeled to assess the development and the optimization of a controlled drive based on the use of electrostrictive polymers. The monofilament is considered as a viscoelastic rod. By assuming a ‘sliding thread’ deformation occurring within the system, the variation of the monofilament length during the uniform contraction and force generated during a uniaxial mode of actuation have been obtained. The distribution of the axial stress was determined along the length of the monofilament at various stages during the uniform contraction. The rate of contraction reaches a maximum, together with a minimum of the stress intensity when the equivalent Poisson’s ratio of the actuator is negative.

Incorporating an Integral equation for characteristic functions in investigating a class of distributions

Integral equations of characteristic functions are very strong analytical tools for investigating the distributions of stochastic models. The paper makes use of an integral equation, incorporating the characteristic function of a renewal distribution and the characteristic function of a uniform random contraction, for establishing a characterization of a class of selfdecomposable distributions. Moreover, the paper establishes interpretations in stochastic modeling of risk severity reduction operations of the uniform random contraction and the characterization of that class of selfdecomposable distributions.

PP‐13 FATIGUE RATE INDEX IS HIGHER IN CHILDREN WITH FUNCTIONAL CONSTIPATION AND RETENTIVE FECAL INCONTINENCE

Introduction:The fatigue rate index (FRI) is a parameter in anorectal manometry (ARM) to assess sustained voluntary contraction, considering the squeeze pressure and fatigability of the external anal sphincter. It is used in adults to detect fecal incontinence even in patients who present normal squeeze pressures. The FRI in adult patients with functional constipation is similar to controls1.The aim of this preliminary study was to evaluate the feasibility and values of FRI in children with retentive fecal incontinence secondary to functional constipation.Methods:This retrospective study evaluated 105 ARM performed from Jan 2014 to Apr 2015. 42 patients were selected (were able to perform a voluntary contraction and had no co‐morbidities other than functional constipation). 14 of those (33,3%) collaborated in sustaining contraction for 40 seconds (s), allowing the evaluation of the FRI. Patients with retentive fecal incontinence secondary to functional constipation (n = 7, aged 6 to 13 years, 6 boys) were our interest group. Patients with functional constipation without fecal incontinence (n = 7, aged 6 to 13 years, 4 boys) were considered a reference group. The ARM were performed with a radial eight‐channel perfusion catheter (Dynamed™, São Paulo, Brazil) and the FRI was calculated (Proctomaster 6.4) in the first 20 s and overall 40 s of sustained voluntary contraction.Results:In the first 20 s of contraction, the fecal incontinence group showed a significantly higher mean FRI (2.48 ± 1.39 min) compared to the reference group (1.13 ± 0.72 min, p = 0.042), which was not observed in the 40 s due to less uniform contraction. The anal resting pressure was higher in fecal incontinence group (76.83 mmHg) than in the reference group (54.13 mmHg), but the statistical study did not reach significance (p = 0.051).Discussion:The mean FRI obtained in this study is lower than the reported in constipated adults (2,8 min).We hypothesized that the higher FRI found in children with retentive fecal incontinence may be associated with retention behavior in cases of severe constipation and to higher anal resting pressure in patients with retentive incontinence.Conclusions:FRI may be feasible in older children, its reference value may be lower than in adults and it is higher among patients with retentive incontinence.

Uniform Contraction-Expansion Description of Relative Centromere and Telomere Motion

Internal organization and dynamics of the eukaryotic nucleus have been at the front of biophysical research in recent years. It is believed that both dynamics and location of chromatin segments are crucial for genetic regulation. Here we study the relative motion between centromeres and telomeres at various distances and at times relevant for genetic activity. Using live-imaging fluorescent microscopy coupled to stochastic analysis of relative trajectories, we find that the interlocus motion is distance-dependent with a varying fractional memory. In addition to short-range constraining, we also observe long-range anisotropic-enhanced parallel diffusion, which contradicts the expectation for classic viscoelastic systems. This motion is linked to uniform expansion and contraction of chromatin in the nucleus, and leads us to define and measure a new (to our knowledge) uniform contraction-expansion diffusion coefficient that enriches the contemporary picture of nuclear behavior. Finally, differences between loci types suggest that different sites along the genome experience distinctive coupling to the nucleoplasm environment at all scales.

Delineating the inner bladder surface using uniform contractions from the outer surface under variable bladder filling conditions.

To evaluate the methods to delineate the inner bladder (IB) surface using a uniform contraction from the outer bladder (OB) surface, assuming the bladder wall (BW) is either of constant thickness, constant volume or variable volume. 14 prostate intensity-modulated radiotherapy patients with 2 planning CTs were identified. For both CTs, OB was delineated using model-based segmentation. IB was delineated manually. Then, using uniform contractions from OB, the position of IB was approximated using a: 2.5-mm contraction, patient-specific contraction, patient-specific constant wall volume method and variable wall volume method. The structures created using those strategies were compared against the manual IB contours using geometric and dosimetric indices. In the presence of variable bladder filling, use of a generic or patient-specific constant contraction resulted in a significant overestimation of IB volume (+12 and +13 cm(3), respectively; p < 0.001) that was inversely correlated with the difference in urine volume between the scans (R(2) > 0.86). Mean differences across 95% of IB surfaces were ≤2 mm for methods using either constant or variable wall volume. Mean dose-volume histogram (DVH) differences were <1 cm(3) across the whole BW DVH when using the method that assumed a variable wall volume. The variable volume BW model provided the best approximation of the IB surface position under varying filling conditions, based on geometric and dosimetric indices. Use of the equation derived in this research provides a quick and accurate method to delineate the hollow BW on serial imaging for the purposes of dose reconstruction.

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions

In this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn---Hilliard equation.

Why is cytoskeletal contraction required for cardiac fusion before but not after looping begins?

Cytoskeletal contraction is crucial to numerous morphogenetic processes, but its role in early heart development is poorly understood. Studies in chick embryos have shown that inhibiting myosin-II-based contraction prior to Hamburger–Hamilton (HH) stage 10 (33 h incubation) impedes fusion of the mesodermal heart fields that create the primitive heart tube (HT), as well as the ensuing process of cardiac looping. If contraction is inhibited at or after looping begins at HH10, however, fusion and looping proceed relatively normally. To explore the mechanisms behind this seemingly fundamental change in behavior, we measured spatiotemporal distributions of tissue stiffness, stress, and strain around the anterior intestinal portal (AIP), the opening to the foregut where contraction and cardiac fusion occur. The results indicate that stiffness and tangential tension decreased bilaterally along the AIP with distance from the embryonic midline. The gradients in stiffness and tension, as well as strain rate, increased to peaks at HH9 (30 h) and decreased afterward. Exposure to the myosin II inhibitor blebbistatin reduced these effects, suggesting that they are mainly generated by active cytoskeletal contraction, and finite-element modeling indicates that the measured mechanical gradients are consistent with a relatively uniform contraction of the endodermal layer in conjunction with constraints imposed by the attached mesoderm. Taken together, our results suggest that, before HH10, endodermal contraction pulls the bilateral heart fields toward the midline where they fuse to create the HT. By HH10, however, the fusion process is far enough along to enable apposing cardiac progenitor cells to keep ‘zipping’ together during looping without the need for continued high contractile forces. These findings should shed new light on a perplexing question in early heart development.

Freeze Drying on Physiological Characteristics and Sensory Quality of Flowers

Drying technique of many ornamental flowers by freeze drying retains the quality and longevity of flowers. In this experiment freeze drying effect on different flowers (rose, carnation, jasmine, orchid and chrysanthemum) for flower colour, flower physiology, tissue integrity and moisture content with dry flower shape were studied. Flowers which recorded optimum moisture loss provided rigidity and uniform cell contraction with shape retention while higher moisture loss resulted in shriveled flowers. Light colour flowers retained colour value compared to dark flowers. The carnation (pink) and jasmine flowers recorded optimum percentage of moisture loss due to freeze drying, which did not affect the pigment concentration and retained the colour and shape. These flowers scored better for quality parameters and found suitable for freeze drying in dry flower industry.

On the density of singular hyperbolic three-dimensional vector fields: a conjecture of Palis

In this note we announce a result for vector fields on three-dimensional manifolds: those who are singular hyperbolic or exhibit a homoclinic tangency form a dense subset of the space of C1-vector fields. This answers a conjecture by Palis. The argument uses an extension for local fibred flows of Mañé and Pujals–Sambarino's theorems about the uniform contraction of one-dimensional dominated bundles.

Parametric Studies on Effect of Trailing Liquid Nitrogen Heat Sink on TIG Welding of Steels

Welding is an efficient material joining process. But the localised temperature rise up to the melting point in the vicinity of arc causes non uniform expansion and contraction resulting in residual stress and distortions. Post weld, Pre weld and in-process methods have been studied to reduce these unwanted effects of welding. A trailing heat sink is one such method. This consists of a cooling agent traversing at a constant distance behind the weld arc. Introduction of a cooling agent is reported to reduce the distortion. A liquid nitrogen jet is used as the cooling agent in the present study. A finite element model developed using Sysweld is used to study the effect of liquid nitrogen heat sink on weld distortions and residual stresses. The finite element model developed is used to make a parametric study on the effect of cooling jet radius, cooling strength and the distance between the jet and weld arc on out of plane distortions and stresses. Comparative study of the effect of cooling jet is made for mild steel (MS) and stainless steel (SS). It is observed that the out of plane distortions reduce with increasing cooling strength, jet radius. Reduction in distance between the jet and weld arc also causes a reduction in distortions.

Extensions of contractions and uniform contractions on dense subspaces

We give two extension theorems, which state conditions under which a (uniform) contraction from a dense subspace of a convergence approach space (approach uniform convergence space) to a convergence approach space (approach uniform convergence space) can be extended to a (uniform) contraction defined on the whole space. In order to derive these extension theorems we define and study certain diagonal axioms and the concept of uniform regularity for approach uniform convergence spaces.

A Computational Study of Blebbing in Lipid Membranes

Blebs are membrane protrusions that appear during several physiological processes in eukaryotic cells. The phase behavior and kinetics of blebbing in cellular membrane is investigated computationally using a particle-based model for self-assembled lipid vesicles apposed to an elastic meshwork, mimicking a cell's cytoskeleton. We found that blebbing is induced when the cytoskeleton is subjected to a localized ablation, detachment from the membrane, or a uniform contraction. These results are in good agreement with experiments.

Computational Studies of Blebbing and Vesiculation via Weak Adhesion of the Cytoskeleton in an Erythrocyte Model

Utilizing an implicit-solvent molecular dynamics model [1], we investigated blebbing and vesiculation of the membrane-cytoskeleton complex. Blebs are extracellular balloon-like protrusion, void of cytoskeleton, which appear during cellular processes such as apoptosis, cytokinesis and cell motility. Our computational model for the lipid bilayer-cytoskeleton complex corresponds to a spherical self-assembled lipid vesicles, approximately ninety to three hundred nanometers in size, with an underlying cytoskeleton network, akin to that of erythrocytes. Two main parameters are varied in this study: (1) the ratio of the preferred membrane to cytoskeleton areas, and (2) the adhesion strength of the cytoskeleton network underpinning the membrane. Our previous work [2] established the phase behavior of blebbing with nearly permanent anchoring of the cytoskeleton-membrane complex. Further investigation has shown that blebbing can be induced by local ablation of the cytoskeleton, its peeling from the lipid bilayer and its uniform contraction. The addition of a uniformly weak and reversible adhesion between the cytoskeleton and the lipid bilayer to the model, lead to a depression of the phase behavior, and, furthermore, a vesiculation pathway due to localized decoupling between the bilayer and the cytoskeleton meshwork, which (1) modifies the ratio of preferred membrane to cytoskeleton areas, (2) induces reattachment of the cytoskeleton to the lipid bilayer, which shrinks the neck of the bleb, and (3) leads to an eventual vesiculation of the blebs. The present study may explain the vesiculation in red blood cells during their aging.[1] J.D. Revalee, M. Laradji and P.B. Sunil Kumar, J. Chem. Phys. 128, 035102 (2008)[2] E.J. Spangler, C.W. Harvey, J.D. Revalee, P.B. Sunil Kumar, and M. Laradji, Phys. Rev. E 84, 051906 (2011).

Interplay of octahedral rotations and breathing distortions in charge-ordering perovskite oxides

We investigate the structure--property relationships in $AB$O$_3$ perovskites exhibiting octahedral rotations and cooperative octahedral breathing distortions (CBD) using group theoretical methods. Rotations of octahedra are ubiquitous in the perovskite family, while the appearance of breathing distortions -- oxygen displacement patterns that lead to approximately uniform dilation and contraction of the $B$O$_6$ octahedra -- are rarer in compositions with a single, chemically unique $B$-site. The presence of a CBD relies on electronic instabilities of the $B$-site cations, either orbital degeneracies or valence-state fluctuations, and often appear concomitant with charge order metal--insulator transitions or $B$-site cation ordering. We enumerate the structural variants obtained from rotational and breathing lattice modes and formulate a general Landau functional describing their interaction. We use this information and combine it with statistical correlation techniques to evaluate the role of atomic scale distortions on the critical temperatures in representative charge ordering nickelate and bismuthate perovskites. Our results provide new microscopic insights into the underlying structure--property interactions across electronic and magnetic phase boundaries, suggesting plausible routes to tailor the behavior of functional oxides by design.

Uniform contraction of high-aspect-ratio nanochannels in hexagonally patterned anodic alumina films by pulsed voltage oxidation

Nanopore diameters in porous anodic alumina films were uniformly reduced via facile pulsed voltage anodization method. Spontaneous self-ordering into hexagonal pattern was maintained at pulse frequencies of 0.5–1Hz in both 0.3M oxalic (long-range ordered domains) and 10wt.% sulphuric (incipient short range ordering) acids, and yielded smooth uniform nanochannels of 19±2nm and 8±1nm diameters correspondingly.