Order In Expansion Research Articles

Експандерна реконструкція тканин у дітей із пігментними та судинними новоутвореннями

The main indications for surgical treatment of congenital nevi and vascular malformations of superficial tissues are the reduction of psychosocial problems (58%) and the achievement of aesthetic improvement (51%). In the case of large lesions, the problem is the replacement of large tissue defects, which can be solved using tissue expanders. Aim - establishing the effectiveness and safety of expander reconstruction of surface tissues after removal of large and giant pigment and vascular lesions. Materials and methods. We performed a retrospective study of 8 patients undergoing superficial tissues expander reconstruction in National children hospital OKHMATDYT in the period 2019-2023. Preoperative planning was carried out in order to determine the shape, size and volume of the expander. The aim of the first operative intervention was the placement of the expander. During the second planned operation, the expander was removed, the walls of the formed capsule were damaged, a pigment or vascular lesions was completely or partially removed, and the formed flap was moved to the site of the tissue defect. Results. 19 expanders were used in 8 children for the following indications: congenital nevi (n=6) and vascular malformations (n=2). The age of patients at the time of treatment was from 3 to 17 years. From 1 to 6 expanders were placed in patients. Round (n=1), rectangular (n=10), and sickle-shaped (n=8) expanders were used, the volume of expanders was from 100 to 500 ml. The duration of tissue expansion ranged from 34 to 63 days, on average 43±19. Complete removal of lesions was achieved in 6 (75%) patients, partial removal in 2 (10.5%). Complications that led to the removal of the expander occurred in 2 (10.5%) cases, in particular, hematoma and infection in the area of the scalp and in 1 (5%) case on the background of Herpes zoster infection. Conclusions. Tissue expansions in order to replace large defects after the removal of pigmented and vascular lesions is safe, effective and aesthetic, as it ensures the replacement of the defect with homogeneous tissues. The overall complication rate was 10.5%. Limitation of tissue expansion use is the young age of the child, skin damage and insufficient area of healthy tissue. The research was carried out in accordance with the principles of the Helsinki Declaration. The study protocol was approved by the Local Ethics Committee of participating institution. The informed consent of the patient was obtained for conducting the studies. No conflict of interest was declared by the authors.

Supersonic turbulence simulations with GPU-based high-order Discontinuous Galerkin hydrodynamics

ABSTRACT We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is known to efficiently produce accurate results for smooth problems (exponential convergence with expansion order), physical discontinuities in solutions, like shocks, prove challenging and may significantly diminish DG’s applicability to practical astrophysical applications. We consider whether DG is able to retain its accuracy and stability for highly supersonic turbulence, characterized by a network of shocks. We find that our new implementation, which regularizes shocks at subcell resolution with artificial viscosity, still performs well compared to standard second-order schemes for moderately high-Mach number turbulence, provided we also employ an additional projection of the primitive variables on to the polynomial basis to regularize the extrapolated values at cell interfaces. However, the accuracy advantage of DG diminishes significantly in the highly supersonic regime. Nevertheless, in turbulence simulations with a wide dynamic range that start with supersonic Mach numbers and can resolve the sonic point, the low-numerical dissipation of DG schemes still proves advantageous in the subsonic regime. Our results thus support the practical applicability of DG schemes for demanding astrophysical problems that involve strong shocks and turbulence, such as star formation in the interstellar medium. We also discuss the substantial computational cost of DG when going to high order, which needs to be weighted against the resulting accuracy gain. For problems containing shocks, this favours the use of comparatively low DG order.

Diffeomorphisms of the energy-momentum space: Perturbative QED

A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of noncommutativity: the Snyder model and the so called GUP models. For the Snyder model it is shown that all the amplitudes are finite at every order of the perturbation expansion.

Numerical accuracy of the derivative-expansion-based functional renormalization group

Abstract We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized renormalization group transformation. For this purpose, we implement the local potential approximation and O ( ∂ 2 ) orders of the derivative expansion for the three-dimensional O(N) models with N ∈ { 1 , 2 , 3 } . We identify several categories of numerical error and devise simple tests to track their magnitude as functions of numerical parameters. Our numerical schemes converge properly and are characterized by errors of several orders of magnitude smaller than the error bars of the derivative expansion for these models. We highlight situations in which our methods cease to converge, most often due to rounding errors. In particular, we observe an impaired convergence of the discretization scheme when the ρ ~ grid is cut off at the value ρ ~ Max smaller than 3.5 times the local potential minimum. The program performing the numerical calculations for this study is shared as an open-source library accessible for review and reuse.

The quantum spectral method: from atomic orbitals to classical self-force

Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the Quantum Spectral Method, is based on a novel application of Bohr’s correspondence principle, obtaining non-perturbative classical dynamics as the classical limit of quantum matrix elements. A major application of our method is the calculation of self-force as the classical limit of atomic radiative transitions. We demonstrate this by calculating an adiabatic electromagnetic inspiral, along with its associated radiation, at all orders in the multipole expansion. Finally, we propose a future application of the Quantum Spectral Method to compute scalar and gravitational self-force in Schwarzschild, analytically.

Producing fully-charmed tetraquarks via charm quark fragmentation in colliders

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an S-wave fully-charmed tetraquark, denoted as T4c. The charm-to-T4c fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in αs expansion. The LDMEs are approximated using the T4c four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-T4c fragmentation function, we predict the T4c production rate at high transverse momentum pT regime in colliders. Both the differential distribution over pT and the integrated cross sections are predicted at the LHC. The cross sections for T4c states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for T4c event production at the LHC. Additionally, we estimate for the photoproduction of T4c in electron-proton (ep) collisions. It is observed that the cross sections for these processes are moderate at the HERA and EIC, and relatively small at the EicC. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at ep colliders is somewhat challenging.

Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an Mth-order diagram at inverse temperature β and spectral width ωmax from O((βωmax)2M−1) for a direct quadrature to O(M(log(βωmax))M+1), with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca2RuO4, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. Published by the American Physical Society 2024

Integrability of large-charge sectors in generic 2D EFTs

It is shown that integrability is an accidental property of generic two-dimensional O(2)-symmetric asymptotically-free theories in the regime where the charge density is much larger than the dynamical scale. We show this by constructing an infinite tower of higher-spin conserved currents in the most generic effective Lagrangian at large chemical potential to all orders in perturbative expansion in the renormalization-group invariant coupling constant.

Derivation and error analysis of three-level linearized difference schemes for solving the Burgers-Fisher equation

ABSTRACT The main scope of this paper is to develop and analyse three-level linearized difference schemes for solving the classical Burgers-Fisher equation. For the Dirichlet boundary value problem, the first three-level linearized difference scheme is second-order accurate in both time and space. It is able to obey a discrete conservative law. By the discrete energy argument and induction, it is rigorously proved to be uniquely solvable and unconditionally convergent. Furthermore, with the purpose of improving the numerical accuracy in space, another three-level linearized compact difference scheme is then established together with some investigation on its discrete conservation law, unique solvability and unconditional convergence of order two in time and four in space. The coupled nonlinearity of Burgers' type and Fisher type is intensively treated via the order of reduction and Taylor expansion. In addition, extensions to the problem subject to the periodic boundary condition (PBC) are involved. To the best of our knowledge, this is a rare work to carefully design and rigorously analyse the high-order linearized difference schemes for solving the Burgers-Fisher equation. Numerical tests are provided to support the theoretical results and to verify the computational efficiency.

Computing NMHV gravity amplitudes at infinity

In this note we show how the solutions to the scattering equations in the NMHV sector fully decompose into subsectors in the z → ∞ limit of a Risager deformation. Each subsector is characterized by the punctures that coalesce in the limit. This naturally decomposes the E(n − 3, 1) solutions into sets characterized by partitions of n − 3 elements so that exactly one subset has more than one element. We present analytic expressions for the leading order of the solutions in an expansion around infinite z for any n. We also give a simple algorithm for numerically computing arbitrarily high orders in the same expansion. As a consequence, one has the ability to compute Yang-Mills and gravity amplitudes purely from this expansion around infinity. Moreover, we present a new analytic computation of the residue at infinity of the n = 12 NMHV tree-level gravity amplitude which agrees with the results of Conde and Rajabi. In fact, we present the analytic form of the leading order in 1/z of the Cachazo-Skinner-Mason/CHY formula for graviton amplitudes for each subsector and to all multiplicity. As a byproduct of the all-order algorithm, one has access to the numerical value of the residue at infinity for any n and hence to the corrected CSW (or MHV) expansion for NMHV gravity amplitudes.

Religious Orders' Impact on Medieval Europe: Origins, Influence, and Significance: A Literature Review

In summary, this literature review has offered a comprehensive exploration of the origins and evolution of medieval religious orders. We've traced the pioneering efforts of figures such as the Desert Fathers and Irish monks, who embarked on radical ascetic experiments. From these early efforts, coenobitic rules emerged, providing structured frameworks for religious life. Notably, the Rule of Benedict played a pivotal role in balancing prayer, labor, study, and moderation. The advent of mendicant orders marked a revival of religious fervor through their commitment to poverty, mobility, and dynamic preaching. The rapid expansion of religious orders was made possible by elite patronage, facilitating their spread across Europe. These orders left indelible marks on education, politics, and culture, shaping medieval life. Religious figures assumed prominent roles as counselors to rulers, influential doctrinal shapers, and builders of educational institutions. By synthesizing scholarship, this review illuminates the multifaceted journey of medieval religious orders, from their humble beginnings to their profound impact on European civilization. It underscores their significance and lays the groundwork for further research on their enduring roles.

Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross–Pitaevskii Regime

Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross–Pitaevskii Regime

Functional renormalization group for “p = 2” like glassy matrices in the planar approximation II. Ward identities method in the deep IR

This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the (U(N))×2 symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.

Soft pattern of gravitational Rutherford scattering from heavy target mass expansion

Abstract We investigate the soft behavior of the tree-level Rutherford scattering processes mediated via $t$-channel one-graviton exchange. We consider two types of Rutherford scattering processes, {\it e.g.}, a low-energy massless structureless projectile (up to spin-$1$) hits a static massive composite particle carrying various spins (up to spin-$2$), and a slowly-moving light projectile hits a heavy static composite target. The unpolarized cross sections in the first type are found to exhibit universal forms at the first two orders in $1/M$ expansion, yet differ at the next-to-next-to-leading order, though some terms at this order still remain universal or depend on the target spin in a definite manner. The unpolarized cross sections in the second type are universal at the lowest order in projectile velocity expansion and through all orders in $1/M$, independent of the spins of both projectile and target. The universality partially breaks down at relative order-$v^2/M^2$, albeit some terms at this order still depend on the target spin in a specific manner.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

A novel method for highly linear gradient coil design based on stream function.

Magnetoencephalography (MEG) and magnetic resonance imaging (MRI) are non-invasive imaging techniques that offer effective means for disease diagnosis. A more straightforward and optimized method is presented for designing gradient coils which are pivotal parts of the above imaging systems. A novel design method based on stream function combining an optimization algorithm is proposed to obtain highly linear gradient coil. Two-dimensional Fourier expansion of the current field on the surface where the coil is located and the equipotential line of the expansion term superposition according to the number of turns of the coil are used to represent the coil shape. Particle swarm optimization is utilized to optimize the coil shape while linearity and field uniformity are used as parameters to evaluate the coil performance. Through this method, the main parameters such as input current distribution region, coil turns, desired magnetic field strength, expansion order and iteration times can be combined in a given solution space to optimize coil design. Simulation results show that the maximum linearity spatial deviation of the designed bi-planar x-gradient coil compared with that of target field method is reduced from 14% to 0.54%, and that of the bi-planar z-gradient coil is reduced from 8.98% to 0.52%. Similarly, that of the cylindrical x-gradient coil is reduced from 2% to 0.1%, and that of the cylindrical z-gradient coil is reduced from 0.87% to 0.45%. The similar results are found in the index of inhomogeneity error. Moreover, it has also been verified experimentally that the result of measured magnetic field is consist with simulated result. The proposed method provides a straightforward way that simplifies the design process and improves the linearity of designed gradient coil, which could be beneficial to realize better magnetic field in engineering applications.

Numerical simulation of wave propagation by using a hybrid method with an arbitrary order accuracy in both spatial and temporal approximations

This paper introduces an innovative numerical methodology designed to achieve high precision solution of acoustic wave propagation problem in isotropic material. During the temporal discretization process, the Krylov deferred correction (KDC) technique is employed, wherein a new variable is introduced to handle the second-order time derivative in the governing equations. An improved strategy is adopted for precisely implementing boundary conditions. Following this, the arbitrary-order generalized finite difference method (GFDM) is employed to simulate the transformed boundary value problem at each time step, enabling our framework to select the Taylor series expansion order arbitrarily. Ultimately, a hybrid numerical approach for wave problems is developed to achieve arbitrary-order accuracy in both spatial and temporal approximations. The developed scheme undergoes validation through four different numerical experiments in two- or three-dimension, wherein the numerical solutions obtained are compared with either analytical solutions or results from COMSOL software.

Estimates on the convergence of expansions at finite baryon chemical potentials

Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Padé approximants, and the T′ expansion proposed recently in lattice QCD simulations, have been investigated in a low energy effective theory within the functional renormalization group approach. It is found that the convergence of the T′ expansion and the Padé approximants is consistent with the conventional Taylor expansion, within the expansion orders considered in this work. Furthermore, we find that the consistent regions of the three different expansions are in agreement with the convergence radius of the Lee-Yang edge singularities. Published by the American Physical Society 2024

The NNLO soft function for N-jettiness in hadronic collisions

We compute the N-jettiness soft function in hadronic collisions to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an extension of the SoftSERVE framework to soft functions that involve an arbitrary number of lightlike Wilson lines. We present numerical results for 1-jettiness and 2-jettiness, and illustrate that our formalism carries over to a generic number of jets by calculating a few benchmark points for 3-jettiness. We also perform a detailed analytic study of the asymptotic behaviour of the soft-function coefficients at the edges of phase space, where one of the jets becomes collinear to another jet or beam direction, and comment on previous calculations of the N-jettiness soft function.

Quadrupolar radiation in de Sitter: displacement memory and Bondi metric

We obtain the closed form expression for the metric perturbation around de Sitter spacetime generated by a matter source below Hubble scale both in generalized harmonic gauge and in Bondi gauge up to quadrupolar order in the multipolar expansion, including both parities (i.e. both mass and current quadrupoles). We demonstrate that such a source causes a displacement memory effect close to future infinity that originates, in the even-parity sector, from a Λ-BMS transition between the two non-radiative regions of future infinity.

The NNLO gluon beam function for jet-veto resummation

We compute the gluon beam function for jet-veto resummation to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an automated framework that was previously used for the computation of the respective quark beam function, and which we significantly extended for the present calculation. In particular, the perturbative matching kernels are directly calculated in momentum space, without the need to perform an additional Mellin transform. We present results for both gluon and quark-initiated processes, which we cross-checked with an independent semi-analytical method that exploits the similarity of the beam functions to the more familiar case of transverse-momentum resummation. Our computation is relevant for jet-veto resummations at NNLL′ accuracy.