Browsing by Subject "EQUATION"

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  • Mäntysaari, Heikki; Schenke, Björn (2020)
    We show how exclusive vector meson production off light ions can be used to probe the spatial distribution of small-x gluons in the deuteron and He-3 wave functions. In particular, we demonstrate how short-range repulsive nucleon-nucleon interactions affect the predicted coherent J/Psi production spectra. Fluctuations of the nucleon substructure are shown to have a significant effect on the incoherent cross section above vertical bar t vertical bar greater than or similar to 0.2 GeV2. By explicitly performing the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution, we predict the x dependence of coherent and incoherent cross sections in the electron-ion collider energy range. In addition to the increase of the average size of the nucleus with decreasing x, both the growth of the nucleons and subnucleonic hot spots are visible in the cross sections. The decreasing length scale of color charge fluctuations with decreasing x is also present, but may not be observable for vertical bar t vertical bar <1 GeV2, if subnucleonic spatial fluctuations are present.
  • Muratore-Ginanneschi, Paolo; Schwieger, Kay (2017)
    We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field.
  • Caro, Pedro; Helin, Tapio; Kujanpää, Antti; Lassas, Matti (2019)
    Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be recovered from empirical correlations between amplitude measurements of the leading singularities, detected in the exterior of a region where the potential is almost surely supported. The result is then applied to show that if two sufficiently regular random fields yield the same correlations, they have identical laws as function-valued random variables.
  • Dumitru, Adrian; Mantysaari, Heikki; Paatelainen, Risto (2022)
    The three point correlation function of color charge densities is evaluated explicitly in light -one gauge for a proton on the light cone. This includes both C-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light -cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent of the renormalization scale. It does, however, exhibit the well-known soft and collinear singularities. The expressions derived here provide the C-odd contribution to the initial conditions for high-energy evolution of the dipole scattering amplitude to small x. Finally, we also present a numerical model estimate of the impact parameter dependence of quantum color charge three-point correlations in the proton at moderately small x.
  • Barrera Vargas, Gerardo; Pardo, Juan Carlos (2020)
    In this paper, we study the cut-off phenomenon under the total variation distance of d-dimensional Ornstein-Uhlenbeck processes which are driven by Lévy processes. That is to say, under the total variation distance, there is an abrupt convergence of the aforementioned process to its equilibrium, i.e. limiting distribution. Despite that the limiting distribution is not explicit, its distributional properties allow us to deduce that a profile function always exists in the reversible cases and it may exist in the non-reversible cases under suitable conditions on the limiting distribution. The cut-off phenomena for the average and superposition processes are also determined.
  • Guerra, André; Koch, Lukas; Lindberg, Sauli (2021)
    We consider the class of planar maps with Jacobian prescribed to be a fixed radially symmetric function f and which, moreover, fixes the boundary of a ball; we then study maps which minimise the 2p-Dirichlet energy in this class. We find a quantity lambda[f] which controls the symmetry, uniqueness and regularity of minimisers: if lambda[f]
  • Biancari, Fausto; Mariscalco, Giovanni; Yusuff, Hakeem; Tsang, Geoffrey; Luthra, Suvitesh; Onorati, Francesco; Francica, Alessandra; Rossetti, Cecilia; Perrotti, Andrea; Chocron, Sidney; Fiore, Antonio; Folliguet, Thierry; Pettinari, Matteo; Dell'Aquila, Angelo M.; Demal, Till; Conradi, Lenard; Detter, Christian; Pol, Marek; Ivak, Peter; Schlosser, Filip; Forlani, Stefano; Chetty, Govind; Harky, Amer; Kuduvalli, Manoj; Field, Mark; Vendramin, Igor; Livi, Ugolino; Rinaldi, Mauro; Ferrante, Luisa; Etz, Christian; Noack, Thilo; Mastrobuoni, Stefano; De Kerchove, Laurent; Jormalainen, Mikko; Laga, Steven; Meuris, Bart; Schepens, Marc; El Dean, Zein; Vento, Antti; Raivio, Peter; Borger, Michael; Juvonen, Tatu (2021)
    Background: Acute Stanford type A aortic dissection (TAAD) is a life-threatening condition. Surgery is usually performed as a salvage procedure and is associated with significant postoperative early mortality and morbidity. Understanding the patient's conditions and treatment strategies which are associated with these adverse events is essential for an appropriate management of acute TAAD. Methods: Nineteen centers of cardiac surgery from seven European countries have collaborated to create a multicentre observational registry (ERTAAD), which will enroll consecutive patients who underwent surgery for acute TAAD from January 2005 to March 2021. Analysis of the impact of patient's comorbidities, conditions at referral, surgical strategies and perioperative treatment on the early and late adverse events will be performed. The investigators have developed a classification of the urgency of the procedure based on the severity of preoperative hemodynamic conditions and malperfusion secondary to acute TAAD. The primary clinical outcomes will be in-hospital mortality, late mortality and reoperations on the aorta. Secondary outcomes will be stroke, acute kidney injury, surgical site infection, reoperation for bleeding, blood transfusion and length of stay in the intensive care unit. Discussion: The analysis of this multicentre registry will allow conclusive results on the prognostic importance of critical preoperative conditions and the value of different treatment strategies to reduce the risk of early adverse events after surgery for acute TAAD. This registry is expected to provide insights into the long-term durability of different strategies of surgical repair for TAAD.
  • Markkanen, Johannes; Yuffa, Alex J. (2017)
    A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles. (C) 2016 Elsevier Ltd. All rights reserved.
  • Lappi, T.; Ramnath, A.; Rummukainen, K.; Weigert, H. (2016)
    We study the effects of a parity-odd "odderon" correlation in Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity-even Pomeron one. This limit increases with N-c, approaching infinity in the infinite N-c limit. We use a systematic extension of the Gaussian approximation including both two-and three-point correlations which enables us to close the system of equations even at finite N-c. In the large-N-c limit we recover an evolution equation derived earlier. By solving this equation numerically we confirm that the odderon amplitude decreases faster in the nonlinear case than in the linear Balitsky-Fadin-Kuraev-Lipatov limit. We also point out that, in the three-point truncation at finite N-c, the presence of an odderon component introduces azimuthal angular correlations similar to cos(n phi) at all n in the target color field. These correlations could potentially have an effect on future studies of multiparticle angular correlations.
  • Rosenström, Tom; Gjerde, Line C.; Krueger, Robert F.; Aggen, Steven H.; Czajkowski, Nikolai Olavi; Gillespie, Nathan A.; Kendler, Kenneth S.; Reichborn-Kjennerud, Ted; Torvik, Fartein K.; Ystrom, Eivind (2019)
    Background Normative and pathological personality traits have rarely been integrated into a joint large-scale structural analysis with psychiatric disorders, although a recent study suggested they entail a common individual differences continuum. Methods We explored the joint factor structure of 11 psychiatric disorders, five personality-disorder trait domains (DSM-5 Section III), and five normative personality trait domains (the 'Big Five') in a population-based sample of 2796 Norwegian twins, aged 19-46. Results Three factors could be interpreted: (i) a general risk factor for all psychopathology, (ii) a risk factor specific to internalizing disorders and traits, and (iii) a risk factor specific to externalizing disorders and traits. Heritability estimates for the three risk factor scores were 48% (95% CI 41-54%), 35% (CI 28-42%), and 37% (CI 31-44%), respectively. All 11 disorders had uniform loadings on the general factor (congruence coefficient of 0.991 with uniformity). Ignoring sign and excluding the openness trait, this uniformity of factor loadings held for all the personality trait domains and all disorders (congruence 0.983). Conclusions Based on our findings, future research should investigate joint etiologic and transdiagnostic models for normative and pathological personality and other psychopathology.
  • Bennaceur, K.; Idini, A.; Dobaczewski, J.; Dobaczewski, P.; Kortelainen, M.; Raimondi, F. (2017)
    We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and selfpairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order and next-to-next-to-leading order, which fairly well describe infinite-nuclearmatter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.
  • Daoxiang, Zhang; Yan, Ping (2019)
    Kooij and Sun (J Math Anal Appl 208:260-276, 1997) proposed a theorem to guarantee the uniqueness of limit cycles for the generalized Lienard system dx/dt=h(y)-F(x),mml:mspace width="4pt"mml:mspacedy/dt=-g(x). We will give a counterexample to their theorem. Moreover, we shall give some sufficient conditions for the existence, uniqueness and hyperbolicity of limit cycles.
  • Solala, Eelis; Losilla, Sergio A.; Sundholm, Dage; Xu, Wenhua; Parkkinen, Pauli (2017)
    We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant threedimensional grid. The bubbles' part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H-2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10(-4) to 10(-7) E-h can be obtained with our approach. Published by AIP Publishing.
  • Fefferman, Charles; Ivanov, Sergei; Kurylev, Yaroslav; Lassas, Matti; Narayanan, Hariharan (2020)
    We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be constructed to approximate a metric space (X, d(X)). This problem is closely related to manifold interpolation (or manifold reconstruction) where a smooth n-dimensional submanifold S subset of R-m, m > n needs to be constructed to approximate a point cloud in Rm. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric. We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary. As an application of the main results, we give a new characterization of Alexandrov spaces with two-sided curvature bounds. Moreover, we characterize the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius. We develop algorithmic procedures that solve the geometric Whitney problem for a metric space and the manifold reconstruction problem in Euclidean space, and estimate the computational complexity of these procedures. The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalization of the Whitney embedding construction where approximative coordinate charts are embedded in R-m and interpolated to a smooth submanifold.
  • Tamminen, J.; Tarvainen, T.; Siltanen, S. (2017)
    The D-bar method at negative energy is numerically implemented. Using the method, we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to diffuse optical tomography, a new way of reconstructing the diffusion coefficient from the associated Complex Geometrics Optics solution is suggested and numerically validated.
  • Boussarie, Renaud; Mäntysaari, Heikki; Salazar, Farid; Schenke, Björn (2021)
    We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small x as a function of the relative momentum P-perpendicular to and momentum imbalance k(perpendicular to) of the dijet system for different photon virtualities Q(2), and study the elliptic and quadrangular anisotropies in the relative angle between P-perpendicular to and k(perpendicular to). We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD) framework, which resums kinematic power corrections of the ratio k(perpendicular to) over the hard scale Q(perpendicular to). By comparing ITMD and CGC results we are able to isolate genuine higher saturation contributions in the ratio Q(s)/Q(perpendicular to) which are resummed only in the CGC. These saturation contributions are in addition to those in the Weizsacker-Williams gluon TMD that appear in powers of Q(s)/k(perpendicular to). We provide numerical estimates of these contributions for inclusive dijet production at the future Electron-Ion Collider, and identify kinematic windows where they can become relevant in the measurement of dijet and dihadron azimuthal correlations. We argue that such measurements will allow the detailed experimental study of both kinematic power corrections and genuine gluon saturation effects.
  • Lappi, T.; Ramnath, A. (2019)
    We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the color glass condensate effective field theory. We discuss a diagrammatic interpretation of the long-range con elators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a Balitsky-Fadin-Kuraev-Lipatov (BFKL) picture in the dilute limit and in momentum space, providing an interpretation of BFKL evolution as a stochastic process for color charges.
  • Ducloue, B.; Iancu, E.; Lappi, T.; Mueller, A. H.; Soyez, G.; Triantafyllopoulos, D. N.; Zhu, Y. (2018)
    We address and solve a puzzle raised by a recent calculation [1] of the cross section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an unreasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by 1 to 2 orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artifact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to momentum space. When used in coordinate space, the running coupling can act as a fictitious potential which mimics hard scattering and thus introduces a spurious contribution to the cross section. We identify a new coordinate-space prescription, which avoids this problem, and leads to results consistent with those obtained with the momentum-space prescription.