Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Layer-by-layer deposition of open-pore mesoporous TiO 2- Nafion® film electrodes

The formation of variable thickness TiO2 nanoparticle-Nafion® composite films with open pores is demonstrated via a layer-by-layer deposition process. Films of about 6 nm diameter TiO2 nanoparticles grow in the presence of Nafion® by “clustering” of nanoparticles into bigger aggregates, and the resulting hierarchical structure thickens with about 25 nm per deposition cycle. Film growth is characterized by electron microscopy, atomic force microscopy, and quartz crystal microbalance techniques. Simultaneous small-angle X-ray scattering and wide-angle X-ray scattering measurements for films before and after calcination demonstrate the effect of Nafion® binder causing aggregation. Electrochemical methods are employed to characterize the electrical conductivity and diffusivity of charge through the TiO2-Nafion® composite films. Characteristic electrochemical responses are observed for cationic redox systems (diheptylviologen2+/+, Ru(NH3)3+/2+6, and ferrocenylmethyl-trimethylammonium2+/+) immobilized into the TiO2-Nafion® nanocomposite material. Charge conduction is dependent on the type of redox system and is proposed to occur either via direct conduction through the TiO2 backbone (at sufficiently negative potentials) or via redox-center-based diffusion/electron hopping (at more positive potentials)

The Role of Alpha 6 Integrin in Prostate Cancer Migration and Bone Pain in a Novel Xenograft Model

Of the estimated 565,650 people in the U.S. who will die of cancer in 2008, almost all will have metastasis. Breast, prostate, kidney, thyroid and lung cancers metastasize to the bone. Tumor cells reside within the bone using integrin type cell adhesion receptors and elicit incapacitating bone pain and fractures. In particular, metastatic human prostate tumors express and cleave the integrin A6, a receptor for extracellular matrix components of the bone, i.e., laminin 332 and laminin 511. More than 50% of all prostate cancer patients develop severe bone pain during their remaining lifetime. One major goal is to prevent or delay cancer induced bone pain. We used a novel xenograft mouse model to directly determine if bone pain could be prevented by blocking the known cleavage of the A6 integrin adhesion receptor. Human tumor cells expressing either the wildtype or mutated A6 integrin were placed within the living bone matrix and 21 days later, integrin expression was confirmed by RT-PCR, radiographs were collected and behavioral measurements of spontaneous and evoked pain performed. All animals independent of integrin status had indistinguishable tumor burden and developed bone loss 21 days after surgery. A comparison of animals containing the wild type or mutated integrin revealed that tumor cells expressing the mutated integrin resulted in a dramatic decrease in bone loss, unicortical or bicortical fractures and a decrease in the ability of tumor cells to reach the epiphyseal plate of the bone. Further, tumor cells within the bone expressing the integrin mutation prevented cancer induced spontaneous flinching, tactile allodynia, and movement evoked pain. Preventing A6 integrin cleavage on the prostate tumor cell surface decreased the migration of tumor cells within the bone and the onset and degree of bone pain and fractures. These results suggest that strategies for blocking the cleavage of the adhesion receptors on the tumor cell surface can significantly prevent cancer induced bone pain and slow disease progression within the bone. Since integrin cleavage is mediated by Urokinase-type Plasminogen Activator (uPA), further work is warranted to test the efficacy of uPA inhibitors for prevention or delay of cancer induced bone pain

Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions

Beyond equilibrium climate sensitivity

ISSN:1752-0908ISSN:1752-089