Search results for "values."
showing 10 items of 1353 documents
The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
2003
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansa…
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
AMYR 2: A new version of a computer program for pair potential calculation of molecular associations
1998
AMYR is a computer program for the calculation of molecular associations using Fraga's pairwise atom-atom potential. The interaction energy is evaluated through a 1R expansion. The electrostatic energy is calculated through either the one-centre-per atom or the three-centres-per atom model by Hunter and Sanders. A pairwise dispersion energy term is included in the potential and corrected by a damping function. The program carries out energy minimizations through variable metric methods. The new version allows for the stationary point analysis of the intermolecular potential by means of the Hessian eigenvalues. Although using low-gradient thresholds optimization procedures to avoid many stat…
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
2018
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…
Effects of BRCA2 cis-regulation in normal breast and cancer risk amongst BRCA2 mutation carriers
2012
Introduction: Cis-acting regulatory single nucleotide polymorphisms (SNPs) at specific loci may modulate penetrance of germline mutations at the same loci by introducing different levels of expression of the wild-type allele. We have previously reported that BRCA2 shows differential allelic expression and we hypothesize that the known variable penetrance of BRCA2 mutations might be associated with this mechanism. Methods: We combined haplotype analysis and differential allelic expression of BRCA2 in breast tissue to identify expression haplotypes and candidate cis-regulatory variants. These candidate variants underwent selection based on in silico predictions for regulatory potential and di…
Journalistic practices of science popularization in the context of users’ agenda: A case study of „New Scientist”
2017
The article includes a discussion of two models which describe contemporary communication processes in journalism: agenda-setting and news value, indicating the need to expand their research tools to include qualitative methods, and merging the analyses of the reception and the message. It also includes indications as to the possibility, or even the social relevance, of the methods for applying those research perspectives to analysing journalism popularising science. Later, I present the results of an analysis of the content of a sample of 500 most read popular science texts available on the New Scientist website. I demonstrate which thematic areas were valued by the readers, and what value…
Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions
2023
We numerically study for the first time the nonlinear GLR-MQ evolution equations for nuclear parton distribution function (nPDFs) to next-to-leading order accuracy and quantify the impact of gluon recombination at small $x$. Using the nCTEQ15 nPDFs as input, we confirm the importance of the nonlinear corrections for small $x \lesssim 10^{-3}$, whose magnitude increases with a decrease of $x$ and an increase of the atomic number $A$. We find that at $x=10^{-5}$ and for heavy nuclei, after the upward evolution from $Q_0=2$ GeV to $Q=10$ GeV, the quark singlet $\Omega(x,Q^2)$ and the gluon $G(x,Q^2)$ distributions become reduced by $9-15$%, respectively. The relative effect is much stronger fo…
The damped harmonic oscillator in deformation quantization
2005
We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson bracket". We determine the eigenstates in the damped regime and compute the transition probability between states of the undamped harmonic oscillator after the system was submitted to dissipation.
Modular invariant dynamics and fermion mass hierarchies around τ = i
2021
We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point $\tau=i$, where modular invariant theories possess a residual $Z_4$ invariance. In this region the breaking of $Z_4$ can be fully described by the spurion $\epsilon \approx \tau - i$, that flips its sign under $Z_4$. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the $Z_4$ symmetry at $\tau=i$, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of $|\epsilon|$. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepto…