Synthesis of chromophores combining second harmonic generation and two photon induced fluorescence properties

The design of new chromophores presenting simultaneous SHG and TPEF properties is reported.     

Structural effects on the ground and excited-state properties of photoswitchable hydrogen-bonding receptors

The ground- and excited-state properties of a series of photochromic barbiturate receptors (N,N'-bis{6-[omega-(anthracen-9-yloxy)alkanoylamino]pyridin-2-yl}-5-t-butyl-isophthalamide, Tn), in which anthracene chromophores are tethered via (CH2)n (n = 1, 3-6) polymethylene linkers to the H-bond receptor moiety, are described. In these systems, the thermally reversible [4pi + 4pi] photodimerization of the anthracenes yields macrocyclic receptors (TnC) that possess significantly reduced affinity toward barbital as compared to their acyclic counterparts. The length of the tether not only determines the overall binding ability of the cyclized receptor but also has a profound influence on the photochemical and photophysical properties of the anthracene chromophores. The reduced mobility experienced by the covalently bound anthracenes controls the reactivity of a fluorescent excimer that is proposed to be an intermediate in the photocyclization process.     

Ricci curvature of Markov chains on metric spaces

We define the coarse Ricci curvature of metric spaces in terms of how much small balls are closer (in Wasserstein transportation distance) than their centers are. This definition naturally extends to any Markov chain on a metric space. For a Riemannian manifold this gives back, after scaling, the value of Ricci curvature of a tangent vector. Examples of positively curved spaces for this definition include the discrete cube and discrete versions of the Ornstein-Uhlenbeck process. Moreover this generalization is consistent with the Bakry-Émery Ricci curvature for Brownian motion with a drift on a Riemannian manifold.Positive Ricci curvature is shown to imply a spectral gap, a Lévy-Gromov-like Gaussian concentration theorem and a kind of modified logarithmic Sobolev inequality. The bounds obtained are sharp in a variety of examples.     

Representing Utility Functions via Weighted Goals

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61–97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy–Boussinesq equations, which is a degenerate version of the Navier–Stokes–Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge–Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375–417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141–1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131–151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20–31, 1991, Arch. Ration. Mech. Anal. 185:341–363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450–1461, 1998; Loeper in SIAM J. Math. Anal. 38:795–823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov–Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29–59, 2001) and of the Keller–Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225–234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819–824, 1992; Chalub et al. in Mon. Math. 142:123–141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier–Stokes–Boussinesq equations. Finally, we show how a “stringy” generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology (see Arnold and Khesin in Topological methods in hydrodynamics. Applied mathematical sciences, vol. 125, Springer, Berlin, 1998; Moffatt in J. Fluid Mech. 159:359–378, 1985, Topological aspects of the dynamics of fluids and plasmas. NATO adv. sci. inst. ser. E, appl. sci., vol. 218, Kluwer, Dordrecht, 1992; Schonbek in Theory of the Navier–Stokes equations, Ser. adv. math. appl. sci., vol. 47, pp. 179–184, World Sci., Singapore, 1998; Vladimirov et al. in J. Fluid Mech. 390:127–150, 1999; Nishiyama in Bull. Inst. Math. Acad. Sin. (N.S.) 2:139–154, 2007).     

Diophantine exponents for mildly restricted approximation

We are studying the Diophantine exponent μ _n,l defined for integers 1≤l<n and a vector α∈ℝ ⁿ by letting

Pressure–velocity coupling allowing acoustic calculation in low Mach number flow

Low Mach number flow computation in co-located grid arrangement requires pressure–velocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure–velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category, the AUSM⁺-up scheme is studied. As an example of the second category, Rhie–Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie–Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure–velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached.     

Variable temperature STM study of Co deposition on a dodecanethiol self assembled monolayer

The present scanning tunneling microscopy study reports on the growth processes of Co vapor-deposited on a dodecanethiol (DDT) self-assembled monolayer (SAM)/Au(111). We observe strongly modified surface and depth diffusions of Co adatoms depending on the growth temperature. Co deposited at 300 K shows an extremely incomplete regime of condensation on the organic layer. Besides, Co penetrates the DDT monolayer and resides at the DDT/Au(111) interface as 2D clusters. This phenomenon takes place through defects in the SAM which are transient channels. In contrast, Co deposited at 50 K shows a complete condensation and nucleates on defects of the SAM layer as 3D islands sitting most likely on top of the DDTs. These results are of interest in the growing field of organic spintronics where the quality of the organic/ferromagnetic interface is a key issue.     

Mueller matrix polarimetry for improved liver fibrosis diagnosis

An experimental Mueller matrix polarimeter is used to quantify human liver fibrosis by measuring retardance and depolarization of thin biopsies. The former parameter is sensitive to fibrillar collagen, the latter is specifically sensitive to fibrillar collagen around blood vessels, which is not significant for liver fibrosis diagnosis. By using depolarization like a filter, retardance distribution enables distinguishing between disease stages and limits the high degree of observer discrepancy.     

Relating the CMSSM and SUGRA models with GUT-scale and super-GUT-scale supersymmetry breaking

While the constrained minimal supersymmetric standard model (CMSSM) with universal gaugino masses, m _1/2, scalar masses, m ₀, and A-terms, A ₀, defined at some high energy scale (usually taken to be the GUT scale) is motivated by general features of supergravity models, it does not carry all of the constraints imposed by minimal supergravity (mSUGRA). In particular, the CMSSM does not impose a relation between the trilinear and bilinear soft supersymmetry breaking terms, B ₀=A ₀?m ₀, nor does it impose the relation between the soft scalar masses and the gravitino mass, m ₀=m _3/2. As a consequence, tanβ is computed given values of the other CMSSM input parameters. By considering a Giudice–Masiero (GM) extension to mSUGRA, one can introduce new parameters to the Kähler potential which are associated with the Higgs sector and recover many of the standard CMSSM predictions. However, depending on the value of A ₀, one may have a gravitino or a neutralino dark matter candidate. We also consider the consequences of imposing the universality conditions above the GUT scale. This GM extension provides a natural UV completion for the CMSSM.