Toftfreeman6899

We consider damped stochastic systems in a controlled (time-varying) potential and study their transition between specified Gibbs-equilibria states in finite time. By the second law of thermodynamics, the minimum amount of work needed to transition from one equilibrium state to another is the difference between the Helmholtz free energy of the two states and can only be achieved by a reversible (infinitely slow) process. The minimal gap between the work needed in a finite-time transition and the work during a reversible one, turns out to equal the square of the optimal mass transport (Wasserstein-2) distance between the two end-point distributions times the inverse of the duration needed for the transition. This result, in fact, relates non-equilibrium optimal control strategies (protocols) to gradient flows of entropy functionals via the Jordan-Kinderlehrer-Otto scheme. The purpose of this paper is to introduce ideas and results from the emerging field of stochastic thermodynamics in the setting of classical regulator theory, and to draw connections and derive such fundamental relations from a control perspective in a multivariable setting.

The mechanical stimulus (i.e. stress or stretch) for growth occurring in the pressure-overloaded left ventricle (LV) is not exactly known.

To address this issue, we investigate the correlation between local ventricular growth (indexed by local wall thickness) and the local acute changes in mechanical stimuli after aortic banding.

LV geometric data were extracted from 3D echo measurements at baseline and 2 weeks in the aortic banding swine model (n = 4). We developed and calibrated animal-specific finite element (FE) model of LV mechanics against pressure and volume waveforms measured at baseline. After the simulation of the acute effects of pressure-overload, the local changes of maximum, mean and minimum myocardial stretches and stresses in three orthogonal material directions (i.e., fiber, sheet and sheet-normal) over a cardiac cycle were quantified. Correlation between mechanical quantities and the corresponding measured local changes in wall thickness was quantified using the Pearson correlation number (PCN) and Spearman rank correlation number (SCN).

At 2 weeks after banding, the average septum thickness decreased from 10.6 ± 2.92mm to 9.49 ± 2.02mm, whereas the LV free-wall thickness increased from 8.69 ± 1.64mm to 9.4 ± 1.22mm. The FE results show strong correlation of growth with the changes in maximum fiber stress (PCN = 0.5471, SCN = 0.5111) and changes in the mean sheet-normal stress (PCN= 0.5266, SCN = 0.5256). Myocardial stretches, however, do not have good correlation with growth.

These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

Elastic fibers are composed primarily of the protein elastin and they provide reversible elasticity to the large arteries. Degradation of elastic fibers is a common histopathology in aortic aneurysms. Pentagalloyl glucose (PGG) has been shown to bind elastin and stabilize elastic fibers in some in vitro studies and in vivo models of abdominal aortic aneurysms, however its effects on native arteries are not well described.

Perform detailed studies of the biomechanical effects of PGG on native arteries and the preventative capabilities of PGG for elastin degraded arteries.

We treated mouse carotid arteries with PGG, elastase (ELA), and PGG+ELA and compared the wall structure, solid mechanics, and fluid transport properties to untreated (UNT) arteries.

We found that PGG alone decreased compliance compared to UNT arteries, but did not affect any other structural or biomechanical measures. Mild (30 sec) ELA treatment caused collapse and fragmentation of the elastic lamellae, plastic deformation, decreased compliance, increased modulus, and increased hydraulic conductance of the arterial wall compared to UNT. PGG+ELA treatment partially protected from all of these changes, in particular the plastic deformation. PGG mechanical protection varied considerably across PGG+ELA samples and appeared to correlate with the structural changes.

Our results provide important considerations for the effects of PGG on native arteries and a baseline for further biomechanical studies on preventative elastic fiber stabilization.

Our results provide important considerations for the effects of PGG on native arteries and a baseline for further biomechanical studies on preventative elastic fiber stabilization.We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent 1 less then m less then ∞ . We first prove the existence of possibly infinitely many bifurcations from the spatially homogeneous steady state. We then focus our attention on the associated free energy, proving existence of minimisers and even uniqueness for sufficiently weak interactions. In the absence of uniqueness, we show that the system exhibits phase transitions we classify values of m and interaction potentials W for which these phase transitions are continuous or discontinuous. Pinometostat in vivo Finally, we comment on the limit m → ∞ and the influence that the presence of a phase transition has on this limit.The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by 'infinity-enhanced Leibniz algebras' defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. We use this observation to streamline the construction of general tensor hierarchies, and we formulate dynamics in terms of a hierarchy of first-order duality relations, including scalar fields with a potential.