General Relation Research Articles

Linear waves at viscoelastic interfaces between viscoelastic media

Many different types of waves that propagate along interfaces are found in nature. We derive the general dispersion relation for interfacial waves along a planar viscoelastic boundary that separates two viscoelastic bulk media, from which the known dispersion relations of different interfacial waves are recovered in the respective parameter limits. Our theory allows us to model acoustic wave-guiding phenomena at biological membranes, where viscoelastic properties are particularly relevant.

The capital logic of platform economy globalisation and it’s critique and transcendence

PurposeTo realise the shared development of the digital economy, people need to transcend the capital logic and advocate the logic of cooperative development, i.e. “co-construction, benefit-sharing and co-governance”. This study aims to discuss the aforementioned statement.Design/methodology/approachPlatform economy is a new economic form produced by the transformation of the social production patterns in the era of digital capitalism. In the neo-imperialist stage, a new stage of capitalist development, capital logic promotes the global expansion of the platform economy and influences its development process, organisational form, contradictions and dilemmas and internal transcendence. Having the spatiotemporal chain of capital circulation repaired, the globalisation of the platform economy is reshaping how the means of production are combined with labour, affecting the local changes in the general relations of production and “international relations of production”.FindingsIn the accumulation of digital capitalism, the social contradictions and fundamental contradictions in the capitalist world have been further intensified, making exploitation, income distribution gap, monopoly and other problems increasingly severe. The imbalance and inequality in the global development of the digital economy are increasingly prominent.Originality/valueRegarding the global governance of the digital economy, China, as a major responsible country, will strive to encourage all countries to co-build a community with a shared future in cyberspace. In the new international development pattern of digital economy globalisation, China must take effective measures to actively safeguard its national security and development interests to meet specific challenges.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 2.07 m with the normalized minor radius 0.2 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

Interaction bulk-boundary relation and its applications towards symmetry breaking and beyond

In this article, we propose a simple but general scaling relation between interactions in a gapped bulk topological matter and gapless interacting surface states. We explicitly illustrate such a generic bulk-boundary relation (BBR) for a few specific interactions in a topological quantum matter, where we can perform dimensional reduction of a microscopic bulk theory to project out interacting surfaces. We have examined renormalization effects of the gapped bulk fermions on the interacting topological surface fermions. As simple applications, we utilize effective interacting quantum fields implied by BBR to explore feasibility of routes to various fascinating emergent phenomena on surfaces including emergent Majorana fermions induced by spontaneous symmetry breaking. We obtain sufficient conditions for these interacting surface phenomena to take place. We have also found that for given bulk electron-phonon interactions and when ${\mathrm{\ensuremath{\Omega}}}_{D}\ensuremath{\ge}m$, the phonon-mediated interactions on the surface are strongest if the bulk Debye frequency ${\mathrm{\ensuremath{\Omega}}}_{D}$ matches $m$, the mass gap of the topological matter.

Operational interpretation of bipartite quantum correlation

Operational interpretations of quantum resource measures lie at the heart of quantum information processing technologies. In this paper, we show that the bipartite quantum correlation in terms of Wigner-Yanase skew information, is the minimal failure probability of a particular state ensemble discrimination task via the associated least square measurement. We then derive a general relation between quantum coherence with respect to quantum operation and discriminating probability specific to least square measurement. Furthermore, we provide a wave-particle duality relation between bipartite quantum correlation and which-path information.

Hydrodynamic heat transport in dielectric crystals in the collective limit and the drifting/driftless velocity conundrum

We apply a recently developed method for solving the linearized phonon Boltzmann equation to study the hydrodynamic thermal transport in dielectrics in the collective limit, i.e., when normal collisions dominate resistive ones. The method recovers Guyer and Krumhansl results for a single Debye branch and extends them to general dispersion relations and branches. Specifically, we obtain explicit microscopic expressions for the phonon distribution and for the transport coefficients in this limit. We find that the phonon distribution differs from the commonly used displaced distribution in two terms: one accounting for viscous flow and another one which allows us to solve a long-standing issue on drifting and driftless second-sound velocities. Thus, the new method allows us to generalize previous results and fill some gaps on fundamental aspects of the collective limit through a simple mathematical formalism. We compare the hydrodynamic framework with previous models and discuss its limitations.

The effects of higher higher-order dispersion on pulse propagation

We give explicit formulas for the propagation of a pulse in a dispersive medium governed by a general dispersion relation. In particular, we consider the mean and standard deviation of a propagating pulse and relate them to the parameters of the initial pulse and the dispersion relation. If the dispersion relation is expanded in a Taylor series, higher-order dispersion is when there are terms that are higher than quadratic. We show the effects of the higher-order dispersion on the propagation of the pulse's mean, standard deviation, and contraction/expansion time. Explicit examples will be given.

The effect of neighboring grain orientation on dislocation-grain interaction in Ti-5553 alloy

The accumulated dislocations are widely reported to be easily transmitted at low angle grain boundaries (GBs), while the associated mechanism at high angle GB needs further investigation. In this paper, the mechanisms associated with the interaction between GBs and 〈111〉 dislocations are investigated in Ti-5553 alloy with body-centered cubic structure. Slip traces transmitted into the neighboring grain or blocked by GBs are observed on the surface of the sample via secondary electron imaging. The corresponding slip system is determined with the combined use of EBSD-detected grain orientation and slip traces. The experimental results indicate that most slips can transfer at low angle GBs, while some slips can also transmit into the neighbor at high angle GBs. The misorientation angle of GBs is invalid to evaluate the mechanism induced by the interaction of dislocations with GBs. Crystallographic alignment-based analysis shows that slip transfer happens at GBs with favorable parameters of high geometric alignment ( m ′) and low residual Burgers vector magnitude (|∆ b |). The general relation of GB misorientation angle with m ′ and |∆ b | is established. The results indicate that low angle GBs always possess high m ′ and low ∆ b , while only some high angle GBs meet the requirement of large alignment parameters. This difference contributes to their preference of slip transfer. Finally, the orientations of best neighboring grains that are favorable for slip transfer are calculated, which is in agreement with the experimentally detected examples. • Dislocations can transmit at some high-angle grain boundaries with special orientations. • General effect of grain boundary misorientation angle on slip transmission is studied. • The best orientations of neighboring grains favorable for slip transmission are established for low- and high-angle GBs.

Reasoning about general preference relations

Preference relations are at the heart of many fundamental concepts in artificial intelligence, ranging from utility comparisons, to defeat among strategies and relative plausibility among states, just to mention a few. Reasoning about such relations has been the object of extensive research and a wealth of formalisms exist to express and reason about them. One such formalism is conditional logic, which focuses on reasoning about the “best” alternatives according to a given preference relation. A “best” alternative is normally interpreted as an alternative that is either maximal (no other alternative is preferred to it) or optimal (it is at least as preferred as all other alternatives). And the preference relation is normally assumed to satisfy strong requirements (typically transitivity and some kind of well-foundedness assumption).Here, we generalize this existing literature in two ways. Firstly, in addition to maximality and optimality, we consider two other interpretations of “best”, which we call unmatchedness and acceptability. Secondly, we do not inherently require the preference relation to satisfy any constraints. Instead, we allow the relation to satisfy any combination of transitivity, totality and anti-symmetry.This allows us to model a wide range of situations, including cases where the lack of constraints stems from a modeled agent being irrational (for example, an agent might have preferences that are neither transitive nor total nor anti-symmetric) or from the interaction of perfectly rational agents (for example, a defeat relation among strategies in a game might be anti-symmetric but not total or transitive).For each interpretation of “best” (maximal, optimal, unmatched or acceptable) and each combination of constraints (transitivity, totality and/or anti-symmetry), we study the sets of valid inferences. Specifically, in all but one case we introduce a sound and strongly complete axiomatization, and in the one remaining case we show that no such axiomatization exists.

Analytic expansions of multi-hadron finite-volume energies. I. Two-particle states

We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of perturbative interactions on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear. We have also developed a Mathematica notebook that automates the expansions described in this work.

Nonlinear hygro-thermo analysis of fluid-conveying cylindrical nanoshells reinforced with carbon nanotubes based on NSGT

This paper studies the vibration analysis of the cylindrical nanoshell reinforced with carbon nanotubes (CNTs) conveying viscous fluid in the hygro-thermal environment for the first time. Nonlocal strain gradient theory (NSGT) is applied to consider the small-scale effect, including both softening and stiffness impacts. First-order shear deformation theory (FSDT) is utilized to study the shear impacts. A general nonlinear relation is applied to study the hygro-thermal effects. To consider the fluid–solid interchange in several environments, Navier–Stokes equations are employed. Hamilton’s principle is utilized to achieve the governing equations of motion. Then, Navier analytical method is applied to derive the natural frequency of the nanoshell with simply-supported boundary conditions. The impacts of several variables are investigated on the vibration characteristics of the CNT cylindrical nanoshell.

Pulse-quality metric for nonstationary partially coherent fields.

This paper generalizes a pulse-quality metric referred to as P2, i.e., the time analogue of Siegman's beam quality factor M2, to include pulsed (nonstationary) random fields of any state of coherence. The analysis begins with the derivation of a general P2 relation, which we then specialize to the important cases of coherent and Schell-model pulsed beams. As examples, we derive the P2 for two stochastic sources: (1) a cosine Gaussian-correlated Schell-model pulsed beam and (2) a nonuniformly correlated pulsed beam. For both of these sources, we generate (in simulation) random instances of each and compare the simulated (Monte Carlo) P2, i.e., computed directly from its definition, to the theoretical quantity. The agreement is excellent, thereby validating our P2 analysis.

Root polytopes and Jaeger‐type dissections for directed graphs

We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, that is, when each cycle has the same number of edges pointing in the two directions. Given a ribbon structure, we identify a natural class of spanning trees and show that, in the semi-balanced case, they induce a shellable dissection of the root polytope into maximal simplices. This allows for a computation of the h ∗ $h^*$ -vector of the polytope and for showing some properties of this new graph invariant, such as a product formula and that in the planar case, the h ∗ $h^*$ -vector is equivalent to the greedoid polynomial of the dual graph. We obtain a general recursion relation as well. We also work out the case of layer-complete directed graphs, where our method recovers a previously known triangulation. Indeed our dissection is often but not always a triangulation; we address this with a series of examples.

Influence of the operation strategy on the energy consumption of an autonomous sensor node

Abstract. Motivated by the application of industry 4.0 and Internet of Things (IoT) technologies, the development of cyber physical systems (CPS) is gaining momentum. As CPS require multiple measurement technologies to drive the intended function, e.g., condition monitoring and in situ measurement, the integration of measurement systems into industrial processes or individual products becomes a critical activity within the development process. Development methods like the V-Model support developers with methodological guidelines, but the related methods and models do not provide sufficient information regarding the energy supply of embedded systems. If the measurement system, consisting of sensor, calculation and communication unit is integrated inside an either sealed or moveable system, e.g., in a gearbox, ensuring a reliable communication and energy supply is a challenging task. This contribution therefore focuses on the energy supply, in particular the electric power consumption of autarchic measurement systems, referred to as sensor nodes. Based on a literature review of existing physical principles determining the energy consumption of semiconductors, a simple estimation model is derived. Estimation models in the current literature mainly focus on the effects of source code or software in general without analyzing a possible impact of operation strategies, such as generic data processing logics in practical applications. The model presented in this contribution is therefore used to identify the energy consumption of sensor nodes influenced by ambient and operating conditions of sensor nodes. Strategies are examined experimentally using an exemplary sensor node, a climatic chamber and a sensor-integrated gearbox as the system to be observed. An analysis of the conducted experiments leads to a more precise model, which is evaluated regarding its significance for predicting the energy consumption and the underlying simplifications. Finally, general relations influencing the energy consumption are presented and necessary research suggested.

Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs only beyond a threshold distance from the origin. This problem is motivated by physical realizations like soft matter under shear, where diffusion of a walk is induced by resetting events of other walks. We first reformulate in the broader context of diffusion with stochastic resetting the so-called Hébraud–Lequeux model for plasticity in dense soft matter, in which diffusivity is proportional to the average resetting rate. Depending on parameter values, the response to a weak external field may be either linear, or non-linear with a non-zero average position for a vanishing applied field, and the transition between these two regimes may be interpreted as a continuous phase transition. Extending the model by considering a general power-law relation between diffusivity and average resetting rate, we notably find a discontinuous phase transition between a finite diffusivity and a vanishing diffusivity in the small field limit.

No general relation between phase vortices and orbital angular momentum

Simple superpositions of Laguerre–Gauss beams illustrate, counterintuitively, the difference between two quantities that are commonly conflated: the component of orbital angular momentum ⟨l⟩ in the propagation direction z, and the total topological charge S, which is the algebraic sum of the charges of vortices piercing any plane perpendicular to z. The examples illustrate two contrasting situations: ⟨l⟩ = 0, S ≠ 0, and ⟨l⟩ ≠ 0, S = 0. In the second situation, not only is the total charge zero but also there are no vortices in the infinite half-space beyond the beam waist plane z = 0.

Do earthworms increase grass biomass production and phosphorus uptake under field conditions?

The key nutrient phosphorus (P) binds strongly to reactive soil particles, which makes it poorly available for plant uptake. In the search for sustainable ways to overcome a resulting P shortage, it has been shown that earthworms can increase the pool of plant available P and enhance plant P uptake under controlled (greenhouse) conditions. To validate these findings under field conditions and to study the effect of earthworm community composition, we conducted a mesocosm-field experiment on grassland. Mesocosms containing a sandy soil with a low P-status and communities of five earthworm species common to the Netherlands (Lumbricus rubellus, Aporrectodea caliginosa, Allolobophora chlorotica, Lumbricus terrestris and Aporrectodea longa; monocultures, three- or five-species mixtures and controls without earthworms) were installed in a field. Aboveground biomass production and P uptake of Lolium perenne were monitored for over two years. Earthworm community composition varied between the start and the end of the experiment, but multiple linear regression on the final earthworm communities yielded strong indications that earthworms increased both biomass production (R2adj = 0.52, p < 0.001, n = 76) and P uptake (R2adj = 0.48, p < 0.001, n = 76). The species A. longa and L. terrestris were most influential for this earthworm effect. We did not observe any general relations between the number of earthworm species in a community and a P effect. Our results suggest that earthworms can indeed increase grass biomass production and P uptake on a low P soil in the field, and can thereby contribute to making the P nutrition of our agricultural systems more sustainable.

A Surface Plasmon–Polariton in a Symmetric Dielectric Waveguide with Active Graphene Plates

A theoretical study of the plasmon modes’ characteristics is carried out in a structure consisting of two active graphene layers separated by a dielectric barrier layer. A general dispersion relation is obtained, the numerical analysis of which reveals the possibility of controlling the parameters of amplified surface modes in the region of graphene negative conductivity. In particular, their dispersion is controlled by changing the chemical potential of the graphene layers. For antisymmetric plasmons, their dependence on the barrier layer parameters was revealed. An increase in the chemical potential makes it possible to expand the region of existence of the amplified plasmons, which is accompanied not only by an increase in the amplification coefficient but also by a shift to the region of higher frequencies of the amplified modes. For the first time, modal bistability was also demonstrated in a limited frequency range for antisymmetric plasmons, due to the appearance of additional modes, in which the phase velocity decreases sharply near the cutoff, and the group velocities of the modes entering the bistability turn out to be opposite in sign. The frequency dependences of the real and imaginary parts of the plasmon propagation constant are analyzed, the distributions of wave fields in the structure are plotted, and the frequency dependence of the depth of the plasmon–polariton is given.

Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control

AbstractThe paper is devoted to a posteriori error identities for the stationary reaction–convection–diffusion problem with mixed Dirichlét–Neumann boundary conditions. They reflect the most general relations between deviations of approximations from the exact solutions and those values that can be observed in a numerical experiment. The identities contain no mesh dependent constants and are valid for any function in the admissible (energy) class. Therefore, the identities and the estimates that follow from them generate universal and fully reliable tools of a posteriori error control.

Generalized uncertainty relations for multiple measurements

The uncertainty relation is regarded as a remarkable feature of quantum mechanics differing from the classical counterpart, and it plays a backbone role in the region of quantum information theory. In principle, the uncertainty relation offers a nontrivial limit to predict the outcome of arbitrarily incompatible observed variables. Therefore, to pursue a more general uncertainty relations ought to be considerably important for obtaining accurate predictions of multi-observable measurement results in genuine multipartite systems. In this article, we derive a generalized entropic uncertainty relation (EUR) for multi-measurement in a multipartite framework. It is proved that the bound we proposed is stronger than the one derived from Renes et al. in [Phys. Rev. Lett. 103,020402(2009) ] for the arbitrary multipartite case. As an illustration, we take several typical scenarios that confirm that our proposed bound outperforms that presented by Renes et al. Hence, we believe our findings provide generalized uncertainty relations with regard to multi-measurement setting, and facilitate the EUR’s applications on quantum precision measurement regarding genuine multipartite systems.