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Casimir operators, abelian subspaces and u-cohomologyMay 15 2007Jun 05 2007This survey paper is an exposition of old and recent results of Kostant and al. on the relationships between the exterior algebra of a simple Lie algebra and the action of the Casimir operator on it. Our exposition relies on u-cohomology and it is basically ... More

The Bruhat order on abelian ideals of Borel subalgebrasJun 22 2018Sep 17 2018Let G be a quasi simple algebraic group over an algebraically closed field k whose characteristic is not very bad for G, and let B be a Borel subgroup of G with Lie algebra b. Given a B-stable abelian subalgebra a of the nilradical of b, we parametrize ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016Apr 12 2017We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal V_k(\mathfrak g^{\natural})$. A particular ... More

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Jul 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

The $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of ZJul 29 2005Apr 08 2006Let an affine Weyl group $\hat W$ act as a group of affine transformations on a real vector space V. We analyze the $\hat W$-orbit of a regular element in V and deduce applications to Kostant's formula for powers of the Euler product and to the representations ... More

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Nov 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

Symmetries of abelian ideals of Borel subalgebrasJan 11 2013Jul 28 2013Elaborating on a paper by Suter, we provide a detailed description of the automorphism group of the poset of abelian ideals in a Borel subalgebra of a finite dimensional complex simple Lie algebra.

ad-nilpotent ideals containing a fixed number of simple root spacesJan 09 2004May 02 2009We give formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a Lie algebra of type B or D containing a fixed number of root spaces attached to simple roots. This result solves positively a conjecture of Panyushev (cf. D. Panyushev, ... More

Abelian subalgebras in Z_2-graded Lie algebras and affine Weyl groupsNov 23 2003Mar 04 2004Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.

Conformal embeddings and simple current extensionsOct 24 2012Feb 18 2014In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.

Dirac operators and the Very Strange Formula for Lie superalgebrasMay 22 2013Aug 04 2013Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.

On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spacesSep 21 2011Mar 31 2012Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We ... More

Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine settingApr 25 2007Oct 02 2007We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting ... More

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairsFeb 18 2011Jan 10 2012We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie ... More

Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z_2-graded Lie algebrasJun 15 2005Jan 23 2006We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian ... More

On the Kernel of the affine Dirac operatorApr 22 2008Sep 14 2009Let L be a finite-dimensional semisimple Lie algebra with a non-degenerate invariant bilinear form, \sigma an elliptic automorphism of L leaving the form invariant, and A a \sigma-invariant reductive subalgebra of L, such that the restriction of the form ... More

Finite vs infinite decompositions in conformal embeddingsSep 22 2015Apr 06 2016Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras $V_{\mathbf{k}}(\mathfrak g^0)\subset V_{k}(\mathfrak g)$, corresponding to an embedding of a maximal equal rank reductive subalgebra $\mathfrak ... More

Kostant's pair of Lie type and conformal embeddingsFeb 08 2018We deal with some aspects of the theory of conformal embeddings of affine vertex algebras, providing a new proof of the Symmetric Space Theorem and a criterion for conformal embeddings of equal rank subalgebras. We finally study some examples of embeddings ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016May 20 2016This paper is a continuation of arXiv:1602.04687. We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural resultsFeb 15 2016Apr 17 2016We find all values of $k\in \mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\mathfrak g,\theta)$ is conformal, where $\mathfrak g$ is a basic simple Lie superalgebra and $-\theta$ its minimal ... More

On classification of non-equal rank affine conformal embeddings and applicationsFeb 20 2017Dec 16 2017We complete the classification of conformal embeddings of a maximally reductive subalgebra $\mathfrak k$ into a simple Lie algebra $\mathfrak g$ at non-integrable non-critical levels $k$ by dealing with the case when $\mathfrak k$ has rank less than that ... More

An application of collapsing levels to the representation theory of affine vertex algebrasJan 30 2018Oct 27 2018We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite module in the category ... More

Toward a Classification of Stochastically Stable Quenched MeasuresMay 27 2002In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in previous paper by Aizenman and Contucci. We show that due to a remarkable cancellation mechanism it reduces to ... More

Approximated methods for the generation of dark matter halo catalogs in the age of precision cosmologyMay 25 2016Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching ... More

Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transitionNov 10 2013Nov 25 2013The two dimensional Coulomb gas is the prototypical model of statistical mechanics displaying a special kind of phase transition, named after Berezinskii, Kosterlitz and Thouless. Physicists and mathematicians proposed several predictions about this system. ... More

Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmologyMay 25 2016Oct 07 2016Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching ... More

Interacting Fermions Picture for Dimer ModelsDec 26 2012May 31 2013Recent numerical results on classical dimers with weak aligning interactions have been theoretically justified via a Coulomb Gas representation of the height random variable. Here we propose a completely different representation, the Interacting Fermions ... More

Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional ModelsDec 01 2012Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean field and finite ... More

Vector and Axial anomaly in the Thirring-Wess modelJan 27 2010Feb 25 2010We study the 2D Vector Meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the ... More

Conformal embeddings in affine vertex superalgebrasMar 09 2019This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra $V_k(\mathfrak g)$ where $\mathfrak g=\mathfrak g_{\bar 0}\oplus ... More

The maximum cardinality of minimal inversion complete sets in finite reflection groupsDec 30 2013Sep 17 2014We compute for reflection groups of type $A,B,D,F_4,H_3$ and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect ... More

On special covariants in the exterior algebra of a simple Lie algebraApr 16 2014Sep 08 2014We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ... More

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systemsNov 27 2015An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw ... More

Optimal control of an Allen-Cahn equation with singular potentials and dynamic boundary conditionDec 11 2012Oct 24 2014In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the cases of distributed ... More

Existence of solutions for a model of microwave heatingMay 13 2015This paper is concerned with a system of differential equations related to a circuit model for microwave heating, complemented by suitable initial and boundary conditions. A RCL circuit with a thermistor is representing the microwave heating process with ... More

Recent advances in bibliometric indexes and the PaperRank problemJul 26 2012Jan 10 2013Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very different intervals. Sometimes, this is evident even within a single given ... More

Monotonicity and Thermodynamic Limit for Short Range Disordered ModelsFeb 06 2003Feb 12 2003If the variance of a short range Gaussian random potential grows like the volume its quenched thermodynamic limit is reached monotonically.

A phase-field approximation of the Willmore flow with volume constraintApr 02 2010The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by a variational ... More

Convergence properties for a generalization of the Caginalp phase field systemMay 28 2012We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a generalization of the ... More

The Allen-Cahn equation with dynamic boundary conditions and mass constraintsMay 01 2014The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside the domain or ... More

Optimal boundary control of a nonstandard Cahn-Hilliard system with dynamic boundary condition and double obstacle inclusionsFeb 07 2017Aug 30 2017In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system ... More

Eigenvalue problems for Fredholm operators with set-valued perturbationsDec 04 2018By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion problem in abstract ... More

Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentialsFeb 18 2015The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting ... More

Variable-step finite difference schemes for the solution of Sturm-Liouville problemsJan 17 2014We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques. Different test ... More

Well-posedness, regularity and asymptotic analyses for a fractional phase field systemJun 12 2018Jun 13 2018This paper is concerned with a non-conserved phase field system of Caginalp type in which the main operators are fractional versions of two fixed linear operators $A$ and $B$. The operators $A$ and $B$ are supposed to be densely defined, unbounded, self-adjoint, ... More

On the Surface Pressure for the Edwards-Anderson ModelJun 03 2003Feb 13 2004For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We find upper and lower bounds uniformly in the volume and show that at ... More

Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditionsJun 28 2012We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic boundary conditions ... More

A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IJul 14 2015In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super Hamiltonian (i.e. ... More

Global existence for a singular phase field system related to a sliding mode control problemJun 25 2017Jul 07 2017In the present contribution we consider a singular phase field system located in a smooth and bounded three-dimensional domain. The entropy balance equation is perturbed by a logarithmic nonlinearity and by the presence of an additional term involving ... More

p-Riesz bases in quasi shift invariant spacesOct 02 2017Let $ 1\leq p< \infty$ and let $\psi\in L^{p}(\R^d)$. We study $p-$Riesz bases of quasi shift invariant spaces $V^p(\psi;Y)$.

"Chaos" in energy futures markets: a controversial matterNov 05 2016In this paper we study the possible "chaotic" nature of some energy and commodity futures time series (like heating oil and natural gas, among the others). In particular the sensitive dependence on initial conditions (the so called "butterfly effect", ... More

A Mathematical Model for Signal's Energy at the Output of an Ideal DACNov 26 2015Mar 21 2016The presented research work considers a mathematical model for energy of the signal at the output of an ideal DAC, in presence of sampling clock jitter. When sampling clock jitter occurs, the energy of the signal at the output of ideal DAC does not satisfies ... More

Modeling and analysis of water-hammer in coaxial pipesJan 29 2015The fluid-structure interaction is studied for a system composed of two coaxial pipes in an annular geometry, for both homogeneous isotropic metal pipes and fiber-reinforced (anisotropic) pipes. Multiple waves, traveling at different speeds and amplitudes, ... More

A phase-field approximation of the Willmore flow with volume and area constraintsApr 19 2012The well-posedness of a phase-field approximation to the Willmore flow with area and volume constraints is established when the functional approximating the area has no critical point satisfying the two constraints. The existence proof relies on the underlying ... More

Scaling Limits for Multispecies Statistical Mechanics Mean-Field ModelsNov 14 2010Jul 06 2011We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to have an exponential distribution of higher order) and ... More

Parallel Factorizations in Numerical AnalysisDec 18 2009In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain ... More

The active and passive populations of Extremely Red ObjectsNov 27 2009Feb 05 2010[abridged] The properties of galaxies with the reddest observed R-K colors (Extremely Red Objects, EROs), including their apparent division into passive and obscured active objects with roughly similar number densities, are a known challenge for models ... More

Bipartite Mean Field Spin Systems. Existence and SolutionOct 03 2007A mean field spin system consisting two interacting groups each with homogeneous interaction coefficients is introduced and studied. Existence of the thermodynamic limit is shown by an asymptotic sub-addittivity method and factorization of correlation ... More

Thermodynamic Limit for Spin Glasses. Beyond the Annealed BoundSep 24 2008Oct 14 2008Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed ... More

UVES-VLT Observations of the OIII Bowen Lines in RR TelDec 15 2000The exceptional resolution of UVES has allowed the detection of weak spectral features and the separation of components in blended lines. The intensities of all of the OIII fluorescence lines produced by the O1, O3 and other channels, including the 5592 ... More

Coherent interaction of a monochromatic gravitational wave with both elastic bodies and electromagnetic circuitsJan 17 1996Aug 26 1998The interaction of a gravitational wave with a system made of an RLC circuit forming one end of a mechanical harmonic oscillator is investigated. We show that, in some configurations, the coherent interaction of the wave with both the mechanical oscillator ... More

Time discretization of a nonlinear phase field system in general domainsNov 26 2018This paper deals with the nonlinear phase field system \begin{equation*} \begin{cases} \partial_t (\theta +\ell \varphi) - \Delta\theta = f & \mbox{in}\ \Omega\times(0, T), \\[1mm] \partial_t \varphi - \Delta\varphi + \xi + \pi(\varphi) = \ell \theta,\ ... More

"Chaos" in energy and commodity markets: a controversial matterNov 05 2016Mar 29 2017We test whether the futures prices of some commodity and energy markets are determined by stochastic rules or exhibit nonlinear deterministic endogenous fluctuations. As for the methodologies, we use the maximal Lyapunov exponents (MLE) and a determinism ... More

A Driver-in-the Loop Fuel Economic Control Strategy for Connected Vehicles in Urban RoadsMay 19 2017In this paper, we focus on developing driver-in-the loop fuel economic control strategy for multiple connected vehicles. The control strategy is considered to work in a driver assistance framework where the controller gives command to a driver to follow ... More

Microscopic modeling and analysis of collective decision making: equality bias leads suboptimal solutionsMar 27 2017We discuss a novel microscopic model for collective decision-making interacting multi-agent systems. In particular we are interested in modeling a well known phenomena in the experimental literature called equality bias, where agents tend to behave in ... More

From the viscous Cahn-Hilliard equation to a regularized forward-backward parabolic equationMay 12 2016A rigorous proof is given for the convergence of the solutions of a viscous Cahn-Hilliard system to the solution of the regularized version of the forward-backward parabolic equation, as the coefficient of the diffusive term goes to 0. Non-homogenous ... More

Solvability and asymptotic analysis of a generalization of the Caginalp phase field systemJul 20 2011Aug 26 2011We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time integration of temperature, and the order parameter. Our analysis ... More

A UV and optical study of 18 old novae with Gaia DR2 distances: mass accretion rates, physical parameters, and MMRDMar 14 2019{We combine the results of our earlier study of the UV characteristics of 18 classical novae (CNe) with data from the literature and with the recent precise distance determinations from the Gaia satellite to investigate the statistical properties of old ... More

Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundaryDec 05 2014The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundary condition, including the Laplace-Beltrami operator on the boundary, the ... More

Cahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn typeMar 12 2018May 16 2018The well-posedness for a system of partial differential equations and dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk $\Omega $ and on the boundary $\Gamma$. The Poisson equation ... More

The class of Lucas-Lehmer polynomialsMar 07 2016In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first ... More

New formulas for $π$ involving infinite nested square roots and Gray codeJun 30 2016Jul 03 2016In previous papers we introduced a class of polynomials which follow the same recursive formula as the Lucas-Lehmer numbers, studying the distribution of their zeros and remarking that this distributions follows a sequence related to the binary Gray code. ... More

Stability theorems for the n-order hold modelsMay 05 2016Aug 08 2016We prove stability results for Gabor frames $\G(g, a,b)$ for a class of functions $g\in L^2(\R)$. Our results can be used to describe the effect of the timing jitters in the p-order hold models of signal reconstruction that are used in electronics and ... More

Ordering of nested square roots of 2 according to Gray codeApr 01 2016In this paper we discuss some relations between zeros of Lucas-Lehmer polynomials and Gray code. We study nested square roots of 2 applying a "binary code" that associates bits $0$ and $1$ to $\oplus$ and $\ominus$ signs in the nested form. This gives ... More

On a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition and its approximation by a Robin boundary conditionMar 22 2018We study a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition, that is, the trace values of the bulk variable and the values of the surface variable are connected via an affine relation, and this serves to generalize the ... More

Deque languages, automata and planar graphsJun 18 2018The memory of a deque (double ended queue) automaton is more general than a queue or two stacks; to avoid overgeneralization, we consider quasi-real-time operation. Normal forms of such automata are given. Deque languages form an AFL but not a full one. ... More

A blind method to recover the mask of a deep galaxy surveyDec 05 2018Feb 19 2019We present a blind method to determine the properties of a foreground contamination, given by a visibility mask, that affects a deep galaxy survey. Angular cross correlations of density fields in different redshift bins are expected to vanish (apart from ... More

Proceedings Eighth International Symposium on Games, Automata, Logics and Formal VerificationSep 06 2017This volume contains the proceedings of the Eighth International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2017). The symposium took place in Roma, Italy, from the 20th to the 22nd of September 2017. The GandALF symposium was ... More

Global Existence of Weak Solutions to a Nonlocal Cahn-Hilliard-Navier-Stokes SystemJan 20 2011Feb 21 2011A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and it has been ... More

Decision Fusion with Unknown Sensor Detection ProbabilityDec 08 2013In this correspondence we study the problem of channel-aware decision fusion when the sensor detection probability is not known at the decision fusion center. Several alternatives proposed in the literature are compared and new fusion rules (namely 'ideal ... More

Correlation Inequalities for Quantum Spin Systems with Quenched Centered DisorderJun 30 2009It is shown that random quantum spin systems with centered disorder satisfy correlation inequalities previously proved (arXiv:cond-mat/0612371) in the classical case. Consequences include monotone approach of pressure and ground state energy to the thermodynamic ... More

On Languages Accepted by P/T Systems Composed of joinsJul 29 2009Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing ... More

Non-erasing Chomsky-Sch{ü}tzenberger theorem with grammar-independent alphabetMay 10 2018The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D \cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is a local language and $h$ ... More

On the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditionsMar 12 2018In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system, which consists ... More

Well-posedness and regularity for a generalized fractional Cahn-Hilliard systemApr 30 2018Oct 21 2018In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous Cahn--Hilliard system in which nonlinearities of double-well type occur. Standard cases like regular or logarithmic potentials, ... More

The Formation of Supermassive Black Holes from Population III.1 Seeds. I. Cosmic Formation Histories and Clustering PropertiesAug 15 2016Nov 29 2018We calculate cosmic distributions in space and time of the formation sites of the first, "Pop III.1" stars, exploring a model in which these are the progenitors of all supermassive black holes (SMBHs), seen in the centers of most large galaxies. Pop III.1 ... More

On a Cahn-Hilliard type phase field system related to tumor growthJan 23 2014Mar 21 2014The paper deals with a phase field system of Cahn-Hilliard type. For positive viscosity coefficients, the authors prove an existence and uniqueness result and study the long time behavior of the solution by assuming the nonlinearities to be rather general. ... More

On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potentialMar 07 2014Sep 26 2014The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard equation, dynamic boundary ... More

A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditionsMar 11 2015A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation, dynamic boundary ... More

Local-field effects on the plasmon dispersion of two-dimensional transition metal dichalcogenidesDec 11 2013Two-dimensional transition-metal dichalcogenides (TMDs) are gaining increasing attention as alternative to graphene for their very high potential in optoelectronics applications. Here we consider two prototypical metallic 2D TMDs, NbSe$_2$ and TaS$_2$. ... More

Analysis and optimal boundary control of a nonstandard system of phase field equationsJan 26 2012Jan 30 2012We investigate a nonstandard phase field model of Cahn-Hilliard type. The model describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in the papers arXiv:1103.4585 and arXiv:1109.3303 ... More

Regularity of the solution to a nonstandard system of phase field equationsMar 13 2013Apr 08 2015A nonstandard system of differential equations describing two-species phase segregation is considered. This system naturally arises in the asymptotic analysis recently done by Colli, Gilardi, Krejci and Sprekels as the diffusion coefficient in the equation ... More

Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: a `deep quench' approachSep 11 2017In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid ... More

Optimal boundary control of a nonstandard viscous Cahn-Hilliard system with dynamic boundary conditionSep 22 2016Sep 07 2017In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of ... More

Optimal distributed control of a generalized fractional Cahn-Hilliard systemJul 09 2018Oct 21 2018In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have been established for a a class of evolutionary systems of two equations having ... More

On a Cahn-Hilliard system with convection and dynamic boundary conditionsApr 18 2017Apr 19 2017This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn-Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the system, is also ... More

Limiting problems for a nonstandard viscous Cahn-Hilliard system with dynamic boundary conditionsFeb 02 2017This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase ... More

On a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition and its approximation by a Robin boundary conditionMar 22 2018Feb 27 2019We study a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition, that is, the trace values of the bulk variable and the values of the surface variable are connected via an affine relation, and this serves to generalize the ... More

The Formation of Supermassive Black Holes from Population III Seeds. I. Cosmic Formation HistoriesAug 15 2016Aug 27 2016We model the cosmic distributions in space and time of the formation sites of the first stars that may be the progenitors of supermassive black holes (SMBHs). Pop III.1 stars are defined to form in dark matter minihalos (i.e., with masses $\sim10^6\:M_\odot$) ... More

An Axiomatic and an Average-Case Analysis of Algorithms and Heuristics for Metric Properties of GraphsApr 05 2016In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an axiomatic framework ... More