Form Of Expansion Research Articles

Correction to: Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach

Correction to: Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach

Theoretical probes of Higgs boson-axion nonperturbative couplings

In this work we investigate the phenomenological implications of several nontrivial Higgs-boson- axion couplings, which cover most of the possible nonperturbative scenarios. Specifically we consider the combination of having higher-order nonrenormalizable Higgs-boson-axion couplings originating from a weakly coupled effective theory combined with nonperturbative couplings of the form ∼εΛc2|H|2cos(ϕfa). Since we consider the misalignment axion, the nonperturbative couplings can be expanded in the form of a perturbation expansion in powers of ϕ/fa, thus after the electroweak symmetry breaking, the effective potential of the axion is drastically affected by these terms. We investigate the phenomenological implications of these terms for various values of the mass scale Λc, and some scenarios are theoretically disfavored, while other scenarios with nonperturbative Higgs-boson-axion couplings of the form ∼εΛc2|H|2cos(ϕfa) with Λc∼10−10×ma and ma∼10−10 eV, lead to a characteristic pattern in the stochastic gravitational wave background via the deformation of the background equation of state parameter occurring at frequencies probed by the Einstein Telescope. We also consider loop effects from the Higgs sector caused by the term ∼εΛc2|H|2cos(ϕfa) if we close the Higgs in one loop. Published by the American Physical Society 2024

Reply to the Comment on “A New Boson Expansion Theory Utilizing a Norm Operator”

Abstract The comment is based on misunderstandings and, as a result, does not evaluate the norm operator method. We refute the comment. The structure of the norm operator composed of all the excitation modes determines whether the form of a practical boson expansion is a small parameter expansion. KT-3 is chimerical. It should be taken seriously that the small parameter expansions do not hold with truncating the contributions of all phonon excitation modes that are not adopted as boson excitations. The formulation using the boson expansion of the projection operator on to the boson vacuum does not allow the limitation of the phonon excitation number beforehand.

Heat equation for Sturm–Liouville operator with singular propagation and potential

Abstract This article considers the initial boundary value problem for the heat equation with the time-dependent Sturm–Liouville operator with singular potentials. To obtain a solution by the method of separation of variables, the problem is reduced to the problem of eigenvalues of the Sturm–Liouville operator. Further on, the solution to the initial boundary value problem is constructed in the form of a Fourier series expansion. A heterogeneous case is also considered. Finally, we establish the well-posedness of the equation in the case when the potential and initial data are distributions, also for singular time-dependent coefficients.

Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: application to T-models

We develop a method to compute the slow-roll expansion for the Hubble parameter in inflationary models in a flat Friedmann-Lemaître-Robertson-Walker spacetime that is applicable to a wide class of potentials including monomial, polynomial, or rational functions of the inflaton, as well as polynomial or rational functions of the exponential of the inflaton. The method, formulated within the Hamilton-Jacobi formalism, adapts the form of the slow-roll expansion to the analytic form of the inflationary potential, thus allowing a consistent order-by-order computation amenable to Padé summation. Using T-models as an example, we show that Padé summation extends the domain of validity of this adapted slow-roll expansion to the end of inflation. Likewise, Padé summation extends the domain of validity of kinetic-dominance asymptotic expansions of the Hubble parameter into the fast-roll regime, where they can be matched to the aforesaid Padé-summed slow-roll expansions. This matching in turn determines the relation between the expansions for the number N of e-folds and allows us to compute the total amount of inflation as a function of the initial data or, conversely, to select initial data that correspond to a fixed total amount of inflation. Using the slow-roll stage expansions, we also derive expansions for the corresponding spectral index ns accurate to order 1/N2, and tensor-to-scalar ratio r accurate to order 1/N3 for these T-models.

Enhanced high-frequency continualization scheme for inertial beam-lattice metamaterials

A multifield continualization technique is introduced that offers a thermodynamically consistent description of the constitutive and dispersive properties of beam-lattice inertial metamaterials with periodic microstructures. The balance equations governing the mechanics of the discrete Lagrangian system are appropriately handled using an innovative continualization scheme to derive an equivalent integral-type continuum model. Based on formal Taylor series expansion of the integral kernels or the corresponding pseudo-differential functions incorporating shift operators and appropriate pseudo-differential downscaling laws, the proposed multifield enhanced continualization scheme allows the derivation of a gradient-type continuum model of given rank and equivalent to lattices. Two different resolution techniques are proposed. Firstly, the corresponding infinite-order average differential equations are tackled using a perturbative approach to describe the forced Bloch wave propagation in the metamaterial. Secondly, higher-order continuum models are employed through proper differential equation truncation to characterize the dispersive properties of the metamaterial in both high- and low-frequency regimes. Moreover, an energetically consistent generalized equivalent Micropolar continua, with non-local inertial terms, are here identified. The multifield continualization procedure is applied to two-dimensional periodic microstructures with tetrachiral, hexachiral, and hexa-tetrachiral topologies. Illustrative examples highlight the ability of the equivalent continuum model to accurately describe the effective constitutive properties of inertial metamaterials with periodic microstructures and to define a dynamic response consistent with the discrete Lagrangian model, validated and tested through virtual experimental verification under free and forced wave conditions.

Genomic Analysis of the Caleosin Family in Theaceae Reveals Lineagespecific Evolutionary Patterns.

Caleosins are recognized as the key proteins found in Lipid Droplets (LDs) and are crucial for the creation, maintenance, and breakdown of LDs. Nevertheless, our understanding of caleosins remains limited within Theaceae, a prominent botanical family encompassing economically significant tea and oil tea species. In this research, we conducted a comprehensive genome-wide exploration and examination of the caleosin family in Theaceae species with sequenced genomes. The gene number of caleosin was similar among Theaceae species. Segmental duplication was the main form of caleosin expansion in Shuchazao (SCZ), Huangdan (HD), Biyun (BY), Tieguanyin (TGY), Longjing (LJ), C. lanceoleosa (Cla) and C. chekiangoleosa (CCH). Synteny analysis revealed one-to-more and more-to-one collinear relationships of caleosin genes among Theaceae species. Caleosins in Theaceae are categorized into either the H-family or the L-family, each exhibiting distinct motif structures and physicochemical properties. Expression analysis revealed an apparent flower-predominant expression pattern of caleosin genes in Theaceae species. In addition, most paralogous pairs displayed expression divergence. This research enhanced our understanding of the lineage-specific evolution of caleosin genes in Theaceae, and is valuable for future functional analysis of this gene family in tea and oil-tea species.

Quasinormal modes of the Mannheim–Kazanas black holes

Abstract A spherically symmetric black hole solution in the conformal Weyl gravity was found by Mannheim and Kazanas in 1988. While the quasinormal modes (QNMs) of these black holes have been considered in a few works, here we complement these studies by considering in detail the regime of vanishing cosmological constant and negative values of the Weyl parameter for which we find quasinormal frequencies for scalar, Dirac and electromagnetic perturbations with the time-domain integration and WKB methods. In particular, we derive the compact and remarkably accurate analytic formula for the frequencies in the form of expansion in terms of the inverse multipole number. Comparison with the time-domain integration shows that the 6th order WKB method with the Padé approximants is quite accurate, unless the black hole is in the near extreme state.

Aggravated commodification as a new dimension of precarity in platform economy

The concepts of precariousness that emerged in Western countries from the 1980s onwards highlight uncertainty regarding the form, scope and nature of labour in the near future. In this article, we use the concept of aggravated commodification as a new dimension of precariousness faced by platform workers. This concept is derived from Polanyi’s idea of fictitious commodities and is treated as a form of labour-market expansion. Applying critically evaluated theory of Karl Polanyi, the article argues that platforms transform labour into a commodity, potentially leading to exploitation and societal unrest. Aggravated commodification refers to work arrangements that introduce (three-sided) market mechanisms within the labour process. Moreover, thanks to the technological infrastructure platforms are leading to the commodification of activities previously performed outside the market and free absorption of activities that were previously a part of wage labour. The study contributes a comprehensive framework for understanding and enriching discussions on precarity in the context of platform capitalism, especially within Central and Eastern European countries.

Spinal Dural Ectasia Spectrum: Management of Two Cases and Systematic Review of the Therapeutic Options.

To describe 2 cases with pathologic expansion of lumbosacral dura mater exerting compression on lumbosacral nerves treated with placement of lumboperitoneal shunt (LPS). Although dural ectasia (DE) is asymptomatic in most cases, a systematic review of the literature was performed focusing on the management when it causes symptoms. Pubmed/Medline and Embase databases were searched for the surgical management of DE. Both pediatric and adult patients were included. The presence of a cerebrospinal fluid leak was considered an exclusion criterion. An additional search was performed to provide a more complete picture of the DE spectrum considering meningoceles as a severe form of dural expansion. Differentiating DE from meningocele, only 20 patients were treated for symptomatic DE. Surgical management varied according to presentation and etiopathogenesis: blood patch or fibrin glue were attempted in case of intracranial hypotension, followed eventually by LPS or marsupialization or dura reduction in cases of failure, whereas LPS or spinal decompression were proposed in cases of radiculopathy or cauda equina syndrome. DE is a rare condition mostly associated with connective tissue disorders. The different etiopathogenesis may explain how it causes symptoms in specific conditions. Treatments should be chosen according to this and may be proposed at the appearance of symptoms since dural expansion is a self-sustained mechanism.

Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach

Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach

Validity of gyrokinetic theory in magnetized plasmas

Gyrokinetics, as a reduced kinetic theory derived from adiabaticity, provides a general framework for the long-term dynamics of magnetized plasmas. While its validity limits are stated in terms of formal expansion parameters, more quantitative test of such is not widely mentioned even if it existed. Here we show, by detailed analyses of the Hamiltonian map with a test particle model, that gyrokinetic theory rests on the inherent nature of particle dynamics as a boundary layer problem. For low-frequency fluctuations, we demonstrate the existence of a frequency-independent threshold in the normalized amplitude, below which gyrokinetics is generally applicable. However, this threshold becomes sensitive to wave parameters in the high-frequency regime, which raises concerns about the generality of high-frequency gyrokinetic theory. Further analyses indicate that constructing a reduced kinetic equation based on superadiabaticity is not feasible. These findings contribute to a deeper understanding of the basic physics behind gyrokinetic theory.

Approximate solutions for the Vlasov–Poisson system with boundary layers

We construct the approximate solutions to the Vlasov–Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov–Poisson system as the parameter goes to zero.

Antiferromagnetic liquid-crystal suspensions of goethite nanorods: three mechanisms of magnetic field influence on orientational structure.

The study looks into magnetically induced orientational transitions in suspensions of goethite nanorods based on a nematic liquid crystal. The study considers magnetically compensated suspension, which is a liquid-crystal analogue of an antiferromagnet. Unlike conventional magnetic particles, goethite nanorods have a remanent magnetic moment directed along the long axis of the particle and also they have negative diamagnetic anisotropy. Thus, it can be claimed that liquid-crystal composites of goethite nanorods have three mechanisms of interaction with an external magnetic field. The first two mechanisms are originally quadrupolar and are related to diamagnetic susceptibility anisotropies of liquid-crystal matrix and impurity goethite nanorods. The third mechanism is a dipolar one and is due to a remanent longitudinal magnetic moment of each dispersed particle. The magnetic-field-induced birefringence is used to show that the presence of three competing orientational mechanisms of interaction with an external magnetic field can both increase and decrease the Fréedericksz transition threshold compared to a pure liquid crystal. Diagrams of orientational phases of the suspension were constructed, and cases of various orientational mechanism predominance were analysed. Besides, a representation of the free energy of the suspension near the Fréedericksz transition in the form of the Landau expansion was obtained. This made it possible to establish that the Fréedericksz transition can occur as a phase transition of both the first and second order.

Development of higher order deterministic approaches of forward and inverse uncertainty quantification for nonlinear engineering systems

This paper introduces an innovative numerical scheme that may accurately quantify the parameter and response distributions with minimal computational costs, with specific applications to the numerical computation of multiphase flows under various fluid conditions. The probabilistic approach of uncertainty quantification, e.g., the Monte Carlo simulation, although known to be effective in estimating the parameter/response distribution for highly nonlinear problems, is usually not applicable to multi-physics and multi-scale integrated systems due to its high computational cost. The objective of this study is first, to reduce the computing demand for complex physical system calculations and, at the same time, to accurately predict actual probability distributions by developing a higher order deterministic approach to uncertainty quantification. To achieve this, instead of executing simulation codes multiple times to estimate the probability distribution, the first to fourth moments of the probability density function are derived directly by employing a second order Taylor expansion form of the responses along with Bayesian statistics. This characterizes the parameter and response distributions computed by inverse and forward uncertainty quantification based on their mean value, mode, covariance, skewness, and kurtosis. The parameter distribution is estimated by the numerically calculated higher moments of the parameters with a posteriori probability density function being derived by Bayesian inference. The parameter distribution is then mapped into the second order approximated response function to compute the characteristics of the response distribution through both analytical calculation and numerical approximation of the moments of the responses. The proposed approach is numerically demonstrated through simulations of two benchmark problems: MIT pressurizer and FEBA tests. The prediction of the responses is improved by inverse uncertainty quantification as numerical calculations with the a posteriori model parameters are in better agreement with the measured data over a wide range of transient periods. Additionally, the response distribution estimated by the proposed approach of forward uncertainty quantification accurately predicts the distribution computed by the Monte Carlo simulation.

The Pathology of Pulmonary Disease After Pediatric Hematopoietic Stem Cell Transplantation.

Pulmonary complications continue to cause significant morbidity and mortality in posthematopoietic stem cell transplantation (HSCT) settings. The histopathology of pulmonary diseases in the post-HSCT context is poorly characterized, especially in the pediatric population. We sought to characterize the pathologic spectrum of pulmonary disease post-HSCT in a pediatric cohort. Fifty-six specimens, including 53 biopsy specimens, corresponding to 53 patients, were identified. Biopsy slides were reviewed and assigned to diagnostic categories (infectious, graft-versus-host disease, vasculopathy, indeterminate, and others) by consensus among 3 pediatric pulmonary pathologists, taking into consideration pathologic, clinical, radiologic, and laboratory findings. The most common diagnostic category was infection (n=20). Vasculopathy, mostly in the form of fibromyxoid intimal expansion, was very common in the entire cohort (n=26) and was the sole finding in a small subset of patients (n=5), with particularly poor outcomes. A subset of biopsies remained indeterminate (n=10), and the findings in this cohort were dominated by acute lung injury. The latter group had a poor prognosis, with a short biopsy-to-death interval. The overall clinicopathologic concordance was 40%, most commonly agreeing in the infectious category. Finally, wedge biopsies led to a change in management in 69% of cases versus 23% of limited procedures (i.e., core needle biopsies). Our results suggest that while infectious complications continue to be common post-HSCT, other findings such as vasculopathy and acute lung injury portend a particularly poor prognosis and should be actively sought and reported.

Spinocerebellar Ataxias: Phenotypic Spectrum of PolyQ versus Non-Repeat Expansion Forms.

Spinocerebellar ataxias (SCA) are most frequently due to (CAG)n (coding for polyglutamine, polyQ) expansions and, less so, to expansion of other oligonucleotide repeats (non-polyQ) or other type of variants (non-repeat expansion SCA). In this study we compared polyQ and non-repeat expansion SCA, in a cohort of patients with hereditary ataxia followed at a tertiary hospital. From a prospective study, 88 patients (51 families) with SCA were selected, 74 (40 families) of whom genetically diagnosed.Thirty-eight patients (51.4%, 19 families) were confirmed as having a polyQ (no other repeat-expansions were identified) and 36 (48.6%, 21 families) a non-repeat expansion SCA. Median age-at-onset was 39.5 [30.0-45.5] for polyQ and 7.0 years [1.00-21.50] for non-repeat expansion SCA. PolyQ SCA were associated with cerebellar onset, and non-repeat expansion forms with non-cerebellar onset. Time to diagnosis was longer for non-repeat expansion SCA. The most common polyQ SCA were Machado-Joseph disease (MJD/SCA3) (73.7%) and SCA2 (15.8%); whereas in non-repeat expansion SCA ATX-CACNA1A (14.3%), ATP1A3-related ataxia, ATX-ITPR1, ATX/HSP-KCNA2, and ATX-PRKCG (9.5% each) predominated. Disease duration (up to inclusion) was significantly higher in non-repeat expansion SCA, but the difference in SARA score was not statistically significant. Cerebellar peduncles and pons atrophy were more common in polyQ ataxias, as was axonal neuropathy.SCA had a wide range of genetic etiology, age-at-onset and presentation. Proportion of polyQ and non-repeat expansion SCA was similar; the latter had a higher genetic heterogeneity. While polyQ ataxias were typically linked to cerebellar onset in adulthood, non-repeat expansion forms associated with early onset and non-cerebellar presentations.

Crowded‐out? Changes in informal childcare during the expansion of formal services in Germany

AbstractInformal childcare care by grandparents, other relatives or friends is an important source of support in many Western countries, including Germany. Yet the role of this type of care is often overlooked in accounts of social policies supporting families with children, which tend to focus on formal childcare. This article examines whether the large formal childcare expansion occurring in Germany in the last two decades has been accompanied by similar or opposite trends in informal childcare usage. It argues that accounting for both formal and informal childcare can offer a more accurate assessment of defamilisation effects of family policies. Drawing on representative data from the German Socio‐Economic Panel the analysis identifies long‐run developments of childcare arrangements for children aged 1–10 between 1997 and 2020, offering for the first time a comprehensive picture of how families with children of different ages mix informal care and service provision. Results show that on average the expansion of formal childcare was not associated with an equal reduction in informal childcare, lending little support to the crowding‐out hypothesis. Further analyses distinguishing between population groups with different propensity to use formal childcare reveal, unexpectedly, remarkable similarities in the use of informal care throughout the period examined. The only exception are families with a migrant background, who tend to use informal childcare less than their counterparts. The general trend is, however, one whereby informal and formal care are increasingly combined.

Stereoselective Access to Diverse Alkaloid-Like Scaffolds via an Oxidation/Double-Mannich Reaction Sequence.

Sequential oxidative cleavage and double-Mannich reactions enable the stereoselective conversion of simple norbornenes into complex alkaloid-like structures. The products undergo a wide range of derivatization reactions, including regioselective enol triflate formation/cross-coupling sequences and highly efficient conversion to an unusual tricyclic 8,5,5-fused lactam. Overall, the process represents a formal one-atom aza-ring expansion with concomitant bridging annulation, making it of interest for the broader derivatization of alkene feedstocks.

Mucin-induced surface dispersal of Staphylococcus aureus and Staphylococcus epidermidis via quorum-sensing dependent and independent mechanisms.

Despite lacking classical motility machinery, nasopharyngeal staphylococci spread rapidly in (peri)oral and respiratory mucosa and cause cross-infections. We describe laboratory conditions for the reproducible study of staphylococcal dispersal on mucosa-like surfaces and the identification of two dispersal stages (colony spreading and dendritic expansion) stimulated by mucin glycoproteins. The mucin type mattered as dispersal required the surfactant activity and hydration provided by some mucin glycoproteins. While colony spreading was a passive mode of dispersal lubricated by the mucins, the more rapid and invasive form of dendritic expansion of Staphylococcus aureus and Staphylococcus epidermidis required additional lubrication by surfactant-active peptides (phenol-soluble modulins) secreted at high cell densities through quorum sensing. These results highlight a hitherto unknown role for gel-forming mucins in the dispersal of staphylococcal strains associated with cross-infections and point at perioral regions as overlooked sources of carriage and infection by staphylococci.