Heat and mass transfer from the mantle: heat flow and He-isotope constraints

Terrestrial heat flow density, q, is inversely correlated with the age, t, of tectono-magmatic activity in the Earth's crust (Polyak and Smirnov, 1966; etc.). «Heat flow-age dependence» indicates unknown temporal heat sources in the interior considered a priori as the mantle-derived diapirs. The validity of this hypothesis is demonstrated by studying the helium isotope ratio, 3He/4He = R, in subsurface fluids. This study discovered the positive correlation between the regionally averaged (background) estimations of R- and q-values (Polyak et al., 1979a). Such a correlation manifests itself in both pan-regional scales (Norhtern Eurasia) and separate regions, e.g., Japan (Sano et al., 1982), Eger Graben (Polyak et al., 1985) Eastern China rifts (Du, 1992), Southern Italy (Italiano et al., 2000), and elsewhere. The R-q relation indicates a coupled heat and mass transfer from the mantle into the crust. From considerations of heat-mass budget this transfer can be provided by the flux consisting of silicate matter rather than He or other volatiles. This conclusion is confirmed by the correlation between 3He/ 4He and 87Sr/86Sr ratios in the products of the volcanic and hydrothermal activity in Italy (Polyak et al., 1979b; Parello et al., 2000) and other places. Migration of any substance through geotemperature field transports thermal energy accumulated within this substance, i.e. represents heat and mass transfer. Therefore, only the coupled analysis of both material and energy aspects of this transfer makes it possible to characterise the process adequately and to decipher an origin of terrestrial heat flow observed in upper parts of the earth crust. An attempt of such kind is made in this paper

Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint. We hope that it is convenient for a reader to have all the methods for different settings in one place. Described methods are based on Mirror Descent algorithm and switching subgradient scheme. One of our focus is to propose, for the listed different settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule. This means that neither stepsize nor stopping rule require to know the Lipschitz constant of the objective or constraint. We also construct Mirror Descent for problems with objective function, which is not Lipschitz continuous, e.g. is a quadratic function. Besides that, we address the problem of recovering the solution of the dual problem

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

Synthesis of a PID-controller of a trim robust control system of an autonomous underwater vehicle

Autonomous underwater vehicles are often used for performing scientific, emergency or other types of missions under harsh conditions and environments, which can have non-stable, variable parameters. So, the problem of developing autonomous underwater vehicle motion control systems, capable of operating properly in random environments, is highly relevant. The paper is dedicated to the synthesis of a PID-controller of a trim robust control system, capable of keeping an underwater vehicle stable during a translation at different angles of attack. In order to synthesize the PID-controller, two problems were solved: a new method of synthesizing a robust controller was developed and a mathematical model of an underwater vehicle motion process was derived. The newly developed mathematical model structure is simpler than others due to acceptance of some of the system parameters as interval ones. The synthesis method is based on a system poles allocation approach and allows providing the necessary transient process quality in a considered system

Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

Global stabilization of fixed points using predictive control

We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev. E54, 1200 (1996)]. We rigorously prove that it is possible to use this method for the global stabilization of a discrete system xn+1=f(xn) into a positive equilibrium for a class of maps commonly used in population dynamics. Moreover, the controlledsystem is globally stable for all values of the control parameter for which it is locally asymptotically stable. Our study highlights the difficulty of obtaining global stability results for other methods of predictive control, where higher iterations of f are used in the control scheme.Ministerio de Ciencia e InnovaciónFondo Europeo de Desarrollo Regiona

The Cinchona Primary Amine-Catalyzed Asymmetric Epoxidation and Hydroperoxidation of α,β-Unsaturated Carbonyl Compounds with Hydrogen Peroxide

Using cinchona alkaloid-derived primary amines as catalysts and aqueous hydrogen peroxide as the oxidant, we have developed highly enantioselective Weitz–Scheffer-type epoxidation and hydroperoxidation reactions of α,β-unsaturated carbonyl compounds (up to 99.5:0.5 er). In this article, we present our full studies on this family of reactions, employing acyclic enones, 5–15-membered cyclic enones, and α-branched enals as substrates. In addition to an expanded scope, synthetic applications of the products are presented. We also report detailed mechanistic investigations of the catalytic intermediates, structure–activity relationships of the cinchona amine catalyst, and rationalization of the absolute stereoselectivity by NMR spectroscopic studies and DFT calculations

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure