Numerical modeling of solar ponds

A SGSP is a basin of water where solar energy is trapped due to an artificially imposed salinity gradient. In a SGSP three zones can be identified: the surface and bottom zones that are both convective and an intermediate zone in between which is intended to be non-convective. This zone acts as a transparent insulation and allows the storage of solar energy at the bottom where it is available for use. A numerical model where the SGSP dynamics is described in terms of velocity, pressure, temperature and salt concentration is presented. It is based on the Navier-Stokes equations for an incompressible fluid coupled to one advection-diffusion equation for and one advection-diffusion equation for . The fluid density is taken to depend on and and the Boussinesq hypothesis is adopted: the fluid density appearing in the LHS of the Navier-Stokes equation is supposed constant and equal to some reference value whereas it is assumed to be variable in the RHS. The space discretization of the governing equations is based on the respective weak formulations and the discretization employs finite elements with a pressure correction method used to decouple velocity and pressure. Integration in time is accomplished by a BDF (Backward Differentiation Formula) method with the above PDEs treated sequentially within each time step. A computer code was developed employing the finite element class library deal.II. Comparisons with available experimental results are made to validate this numerical model

Thermal energy production by a dual solar pound

A Salt Gradient Solar Pond (SGSP) is a salt water basin that collects and stores solar energy. These devices rely on the existence of a non-convective zone (NCZ) that functions as a transparent thermal insulation zone, created by a salt gradient. Salinity and temperature gradients in this zone can give rise to double diffusive problems that can decrease the insulation properties of this zone. The stability of this zone is thus crucial in a SGSP. Stability control, analysis of energy extraction, device efficiency and maintenance strategies are determinant for the correct performance of the SGSP. The implementation of these strategies can be expensive and not sufficient to prevent instability problems. This paper intends to give a contribution to the maintenance problem presenting a new concept of a SGSP utilisation: The Dual Solar Pond (DSP

Statistical stability of equilibrium states for interval maps

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto-t\log|Df(x)|$, for $t$ close to 1. We show that these equilibrium states vary continuously in the weak$^*$ topology within such families. Moreover, in the case $t=1$, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.Comment: More details given and the appendices now incorporated into the rest of the pape

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Extreme value statistics for dynamical systems with noise

We study the distribution of maxima ( extreme value statistics ) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former case, we show that, by perturbing rational or irrational rotations with additive noise, an extreme value law appears, regardless of the intensity of the noise, while unperturbed rotations do not admit such limiting distributions. In the case of deterministic chaotic dynamics, we will consider observables specially designed to study the recurrence properties in the neighbourhood of periodic points. Hence, the exponential limiting law for the distribution of maxima is modified by the presence of the extremal index , a positive parameter not larger than one, whose inverse gives the average size of the clusters of extreme events. The theory predicts that such a parameter is unitary when the system is perturbed randomly. We perform sophisticated numerical tests to assess how strong the impact of noise level is when finite time series are considered. We find agreement with the asymptotic theoretical results but also non-trivial behaviour in the finite range. In particular, our results suggest that, in many applications where finite datasets can be produced or analysed, one must be careful in assuming that the smoothing nature of noise prevails over the underlying deterministic dynamics

Lipophilic Caffeic and Ferulic Acid Derivatives Presenting Cytotoxicity against Human Breast Cancer Cells

In the present work, lipophilic caffeic and ferulic acid derivatives were synthesized, and their cytotoxicity on cultured breast cancer cells was compared. A total of six compounds were initially evaluated: caffeic acid (CA), hexyl caffeate (HC), caffeoylhexylamide (HCA), ferulic acid (FA), hexyl ferulate (HF), and feruloylhexylamide (HFA). Cell proliferation, cell cycle progression, and apoptotic signaling were investigated in three human breast cancer cell lines, including estrogen-sensitive (MCF-7) and insensitive (MDA-MB-231 and HS578T). Furthermore, direct mitochondrial effects of parent and modified compounds were investigated by using isolated liver mitochondria. The results indicated that although the parent compounds presented no cytotoxicity, the new compounds inhibited cell proliferation and induced cell cycle alterations and cell death, with a predominant effect on MCF-7 cells. Interestingly, cell cycle data indicates that effects on nontumor BJ fibroblasts were predominantly cytostatic and not cytotoxic. The parent compounds and derivatives also promoted direct alterations on hepatic mitochondrial bioenergetics, although the most unexpected and never before reported one was that FA induces the mitochondrial permeability transition. The results show that the new caffeic and ferulic acid lipophilic derivatives show increased cytotoxicity toward human breast cancer cell lines, although the magnitude and type of effects appear to be dependent on the cell type. Mitochondrial data had no direct correspondence with effects on intact cells suggesting that this organelle may not be a critical component of the cellular effects observed. The data provide a rational approach to the design of effective cytotoxic lipophilic hydroxycinnamic derivatives that in the future could be profitably applied for chemopreventive and/or chemotherapeutic purposes