Additional Coupling Terms Research Articles

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature

We consider the rigorously derived thin shell membrane \Gamma -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation m\colon \omega\subset \mathbb{R}^{2}\to \mathbb{R}^{3} and the orthogonal microrotation tensor field R\colon \omega\subset \mathbb{R}^{2}\to \operatorname{SO}(3) . The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet-type energy term |\mathrm{D}R|^{2} . We use Rivière’s regularity techniques of harmonic-map-type systems for our system which couples harmonic maps to \operatorname{SO}(3) with a linear equation for m . The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.

Interface reduction technique for Enhanced Craig-Bampton method

Substructure coupling and model order reduction using Component Mode Synthesis (CMS) have, over recent years, gained considerable attention in the vibroacoustic analysis of complex structures. In the CMS methodology, the interior dynamics of each subcomponent in a substructured system are represented by a truncated set of normal modes within the lower frequency range, while all physical degrees of freedom (DOFs) at the interface are retained. In cases where there are many interconnected subcomponents within a system, in particular when these components are finely discretised in the Finite Element (FE) domain, the reduced system matrices may still involve a significant number of equations. This, in turn, leads to a considerable computational workload. To address this issue, further reduction of the system matrices concerning the interface DOFs by using a set of truncated interface modes can be considered. However, the accuracy of the reduced matrices depends on the representation of the truncated dynamics in the reduction process. In this work, two interface reduction techniques are presented to truncate the interface dynamics of the Enhanced Craig-Bampton (ECB) equations of motion. The first technique is a classical interface reduction approach that assumes decoupled internal and interface dynamics. The second approach is an extension of the first one by incorporating an additional coupling term that accounts for interactions between the truncated internal and interface dynamics. The performance of each interface reduction technique is evaluated by applying them to three practical engineering examples. In these instances, resonance frequencies, associated errors, transfer functions, and normal modes are compared to those obtained using both the classical CB method and the full model.

The impact of thermal transport on reactive THMC model for carbon capture and storage

Addressing current limitations in Thermo-Hydro-Mechanical-Chemical (THMC) models is crucial for accurately simulating complex physical and chemical interactions in carbon capture and storage (CCS) processes. This paper presents a new fully coupled THMC model, specifically focusing on investigating thermo-chemo coupling (dissolution) effects for CCS applications. The model is a further extension of the mixture coupling theory, which incorporates entropy and mass balance equations, phenomenological equations, and Maxwell's relations to describe the intricate coupling between mechanical, hydraulic, chemical, and thermal properties. The model considers a two-phase flow, liquid and supercritical. By deriving new coupling terms from the phenomenological equations, the model provides capacity to account for energy losses due to friction between the two phases, along with energy losses arising from the transport of the solute and the evolution of porosity/permeability. Furthermore, the model incorporates an additional coupling term in the mechanical equation to represent the chemical dissolution effect on volumetric strain relief. Two terms added in the liquid equation account for the friction of newly dissolved minerals particles on liquid transport and the effects of porosity changes on liquid flow through dissolution. Finally, Thermal transport coupling is integrated into the model, as it is a crucial part of CCS applications. Numerical results demonstrate that increasing temperature significantly decreases porosity due to thermal expansion, but thermal energy triggers chemical dissolution which in the long run increases both porosity and permeability. Chemical dissolution has the most significant incremental effect on porosity over time, while thermal expansion has the greatest impact until thermal equilibrium is reached, with the direct impacts of pressure and strain on porosity falling in between. This research presents a comprehensive coupling framework that accounts for two-phase friction, the dissolution process, and changing permeability, which gives it potential utility in the planning process for CCS applications.

The Standard Model and quantum state reduction from Heim’s field theory

Abstract Core parts of the Standard Model are derived from B. Heim’s quantum field theory, whose poly-metric describes spacetime and matter in a unified formalism. Its non-linear eigenvalue equation transforms into the Einstein field equation in the macroscopic limit. The 6-dimensional Heim space can be determined as locally isomorphic to a SU(2) ⊗ SU(2) ⊗ U(1) ⊗ U(1) symmetry and thus to the SU(3), which allows to connect to the local gauge symmetries and boson fields of the Standard Model. The Fermion and Higgs field and their coupling are deduced from Heim’s basic equations, providing new insight into possible correlations of these fields. Furthermore, the derivation yields an additional imaginary coupling term which seems to account for quantum mechanical state reduction in the non-relativistic limit. The recently performed calculation of the mass spectrum of elementary particles in a new approach based on Heim’s theory (with average error to the data < 1 % ${< } 1\%$ ) appears as even more relevant, having now shown that the theory can connect to the achievements of the Standard Model.

Vortex merging in ion phase-space induced by two-ion decay instability

We theoretically and numerically study the merger phenomenon of the ion-phase vortex structure in hydrogen plasma. The results indicate that the merging of vortex structures during the nonlinear evolution of ion-acoustic waves (IAW) is mainly due to two-ion decay (TID) instability. When the daughter IAWs of the TID grow to be comparable to the fundamental mode, vortex merging will occur. Furthermore, the vortex merging can abruptly convert the significant energy of the fundamental mode into subharmonic energy, resulting in saturation for the TID of the fundamental mode. After several vortex-merging processes, the system eventually evolves into a turbulent state. In particular, the TID growth rate has been improved by considering two additional second-order coupling terms in this paper, which agree much better with the simulation results. Finally, the importance of the electron kinetic effects in the TID process is also presented by comparing hybrid-Vlasov and full-Vlasov simulations.

Generalization of the Kuramoto model to the Winfree model by a symmetry breaking coupling

We construct a nontrivial generalization of the paradigmatic Kuramoto model by using an additional coupling term that explicitly breaks its rotational symmetry resulting in a variant of the Winfree model. Consequently, we observe the characteristic features of the phase diagrams of both the Kuramoto model and the Winfree model depending on the degree of the symmetry breaking coupling strength for unimodal frequency distribution. The phase diagrams of both the Kuramoto and the Winfree models resemble each other for symmetric bimodal frequency distribution for a range of the symmetry breaking coupling strength except for region shift and difference in the degree of spread of the macroscopic dynamical states and bistable regions. The dynamical transitions in the bistable states are characterized by an abrupt (first-order) transition in both the forward and reverse traces. For asymmetric bimodal frequency distribution, the onset of bistable regions depends on the degree of the asymmetry. Large degree of the symmetry breaking coupling strength promotes the synchronized stationary state, while a large degree of heterogeneity, proportional to the separation between the two central frequencies, facilitates the spread of the incoherent and standing wave states in the phase diagram for a low strength of the symmetry breaking coupling. We deduce the low-dimensional equations of motion for the complex order parameters using the Ott-Antonsen ansatz for both unimodal and bimodal frequency distributions. We also deduce the Hopf, pitchfork, and saddle-node bifurcation curves from the evolution equations for the complex order parameters mediating the dynamical transitions. Simulation results of the original discrete set of equations of the generalized Kuramoto model agree well with the analytical bifurcation curves.

A Mutual Coupling Theory for Arbitrarily Distributed Trimeric Localized Surface Plasmonic Particles

Coupled mode theory (CMT) is widely used to analyze the coupling relationship of plasmons and metasurfaces. However, some details involving coupled structures remain obscure. Herein, the coefficients in CMT are properly defined to solve the problems of inaccurate fitting from two particles to three or more. The proposed improved coupled mode theory (i‐CMT) can perfectly express both the amplitude and phase of transmission curve of dimeric and trimeric mutual coupled systems. A surface plasmonic structure containing multiple metallic spiral structures is fabricated to experimentally verify the accuracy of the i‐CMT. The experimental results are consistent with the theoretical and simulated values, proving the feasibility of using the i‐CMT to analyze and design asymmetric coupled devices. Moreover, the application of the i‐CMT confirms the presence of additional coupling terms in three or more coupled objects, making the calculation of eigenfrequency more accurate.

Phase diagrams of Kitaev models for arbitrary magnetic field orientations

The Kitaev model is an exactly solvable quantum spin model within the language of constrained real fermions. In spite of numerous studies for magnetic fields along special orientations, there is a limited amount of knowledge on the complete field-angle characterization, which can provide valuable information on the existence of fractionalized excitations. For this purpose, we first study the pure ferromagnetic and antiferromagnetic Kitaev models for arbitrary external magnetic field directions via a mean-field theory, showing that there are many topological phases with different (or zero) Chern numbers, depending on the magnetic field strength and orientations. However, a realistic description of the candidate Kitaev materials, within the edge-sharing octahedra paradigm, requires additional coupling terms, including a large off-diagonal term $\mathrm{\ensuremath{\Gamma}}$ along with possible anisotropic corrections ${\mathrm{\ensuremath{\Gamma}}}_{p}$. It is therefore not sufficient to rely on the topological properties of the bare Kitaev model as the basis for the observed thermal Hall-conductivity signals, and an understanding of these extended Kitaev models with a complete field response is demanded. Starting from the zero-field phase diagram of $\mathrm{K}\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}_{p}$ models, we identify, besides the Kitaev spin liquid phase, antiferromagnetic zigzag, ferromagnetic phases, as well as an unusual Kitaev(-$\mathrm{\ensuremath{\Gamma}}$) spin liquid phase. The magnetic field response of these phases for arbitrary field orientations provides a remarkably rich phase diagram. For an extended parameter range and just above the critical field where the zigzag phase is suppressed, there is an intermediate phase region with suppressed energy gaps and substantial spin fractionalization. To comply our findings with experiments, we also reproduce a large asymmetry in the extent of this intermediate phases specifically for the two different field directions $\ensuremath{\theta}=\ifmmode\pm\else\textpm\fi{}{60}^{o}$ with respect to the normal to the plane of the honeycomb lattice.

Synchronization in disordered oscillator lattices: Nonequilibrium phase transition for driven-dissipative bosons

We show that a lattice of phase oscillators with random natural frequencies, described by a generalization of the nearest-neighbor Kuramoto model with an additional cosine coupling term, undergoes a phase transition from a desynchronized to a synchronized state. This model may be derived from the complex Ginzburg-Landau equations describing a disordered lattice of driven-dissipative Bose-Einstein condensates of exciton polaritons. We derive phase diagrams that classify the desynchronized and synchronized states that exist in both one and two dimensions. This is achieved by outlining the connection of the oscillator model to the quantum description of localization of a particle in a random potential through a mapping to a modified Kardar-Parisi-Zhang equation. Our results indicate that long-range order in polariton condensates, and other systems of coupled oscillators, is not destroyed by randomness in their natural frequencies.

Stability of plane Couette flow past an initially stressed solid

In this paper, we carry out linear stability analysis of a coupled solid–fluid system in a plane Couette flow past an initially stressed neo-Hookean solid at creeping flow limit (Re=0) and arbitrary Reynolds number (Re), as well as for different solid thicknesses. In biological and engineering systems, we often encounter flows past initially stressed deformable solids. For these cases, initial strain or initial stress appears as an additional symmetry representing tensor in the constitutive relation. Consequently, initial stress induces anisotropy (transverse isotropy in the present case) and affects material properties. We employ a hyperelastic model for the initially stressed deformable solid to study the effects of both uni-axial and equi-biaxial initial stresses on flow instability. This study also presents a case where anisotropy in the solid interferes with the stability of the solid–fluid coupled system. In contrast with the previous formulations with two or three state Eulerian–Lagrangian formulations, the present formulation requires four configurations for the initially stressed solid, viz. stress-free, initially stressed, deformed, and the perturbed state. This formulation applies to any fluid–solid coupled problems where the solid contains initial/residual stress. Our results show that initial tensile stress stabilizes the flow, while compressive initial stress destabilizes the same. Fortuitously, this observation of coupled fluid–solid stability is in agreement with the stability of solid column-like structures, where compressive axial stress leads to buckling. We report similar results for uni-axial and equi-biaxial initial stress, for different wave modes at creeping flow limit and their extensions at higher Re, and various solid thicknesses. Two modes of instability, viz., short-wave and finite-wave modes present in the creeping-flow limit are significantly affected by tensile/compressive initial stress for both uni-axial and equi-biaxial cases. For uni-axial tensile initial stress, the finite-wave mode does not extend to high Re. Instead of them, we observe multiple upstream modes to become unstable for higher Re, which show the wall mode scaling as O(Re−1/3). These upstream modes are not observed for stress-free solid. This behavior is triggered by the additional coupling terms between initial stress and perturbed variable in the governing equations of initially stressed solids. However, for the equi-biaxial case, the finite-wave mode does extend to higher Re to show wall mode scaling. This mode further stabilizes/destabilizes depending on the tensile/compressive nature of the initial stress present in the solid.

Coleman-De Luccia tunneling wave function with Non-Minimal coupling

We examine a novel method in Coleman-de Luccia vacuum decay analysis by using tunneling wave function approach with additional non-minimal coupling term. Our approach has an advantage that the wave function analysis needs no time dependence, thus consistent with Wheeler-de Witt equation. In the calculation, we use WKB approximation and Hamilton-Jacobi Equation. We discover that the probability of tunneling is lower than the previous study and the tunneling probability depends on both the false and true vacuum state of the scalar field.

A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem

We propose and analyze a stabilized virtual element method for the Stokes problem on polytopal meshes. We employ the $$C^0$$ continuous arbitrary “equal-order” virtual element pairs to approximate both velocity and pressure, and develop a projection-based stabilization term to circumvent the discrete inf-sup condition, then we obtain the corresponding error estimates. The presented method involves neither the projection of the second derivative nor additional coupling terms, and it is parameter-free. In particularly, for the lowest-order case on triangular (tetrahedral) meshes the stabilized method introduced by Bochev et al. (SIAM J. Numer. Anal. 44: 82–101, 2006) is a special case of our method up to an approximation of the load term. Furthermore, numerical results are shown to confirm the theoretical predictions.

Fully Polarizable QM/Fluctuating Charge Approach to Two-Photon Absorption of Aqueous Solutions.

We present the extension of the quantum/classical polarizable fluctuating charge model to the calculation of single residues of quadratic response functions, as required for the computational modeling of two-photon absorption cross sections. By virtue of a variational formulation of the quantum/classical polarizable coupling, we are able to exploit an atomic orbital-based quasienergy formalism to derive the additional coupling terms in the response equations. Our formalism can be extended to the calculation of arbitrary order response functions and their residues. The approach has been applied to the challenging problem of one- and two-photon spectra of rhodamine 6G (R6G) in aqueous solution. Solvent effects on one- and two-photon spectra of R6G in aqueous solution have been analyzed by considering three different approaches, from a continuum (QM/PCM) to two QM/MM models (nonpolarizable QM/TIP3P and polarizable QM/FQ). Both QM/TIP3P and QM/FQ simulated OPA and TPA spectra show that the inclusion of discrete water solvent molecules is essential to increase the agreement between theory and experiment. QM/FQ has been shown to give the best agreement with experiments.

Active Willis metamaterials for ultracompact nonreciprocal linear acoustic devices

Willis materials are complex media characterized by four macroscopic material parameters, the conventional mass density, and bulk modulus and two additional Willis coupling terms, which have been shown to enable unsurpassed control over the propagation of mechanical waves. However, virtually all previous studies on Willis materials involved passive structures which have been shown to have limitations in terms of achievable Willis coupling terms. In this article, we show experimentally that linear active Willis metamaterials breaking these constraints enable highly non-reciprocal sound transport in very subwavelength structures, a feature unachievable through other methods. Furthermore, we present an experimental procedure to extract the effective material parameters expressed in terms of acoustic polarizabilities for media in which the Willis coupling terms are allowed to vary independently. The approach presented here will enable a new generation of Willis materials for enhanced sound control and improved acoustic imaging and signal processing.

An arbitrary multi-node extended multiscale finite element method for thermoelastic problems with polygonal microstructures

A coupling extended multiscale finite element method (P-CEMsFEM) is developed for the numerical analysis of thermoelastic problems with polygonal microstructures. In this method, the polygonal microstructures are effectively represented by polygonal coarse-grid elements and the corresponding numerical base functions are constructed for the temperature and displacement fields, respectively, by a unified method with the corresponding equivalent matrices. To reflect the interaction of deformations among different directions, the additional coupling terms are introduced into the numerical base functions. In addition, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the P-CEMsFEM. Moreover, an arbitrary multi-node strategy is developed to further improve the computational accuracy for the two-dimensional thermoelastic problems. Two types of representative numerical examples are presented. The first type examples are given to testify the proposed multiscale method and the results indicate that the P-CEMsFEM has high accuracy and efficiency for the thermoelastic analysis of heterogeneous multiphase materials and structures. The second type examples testify that the P-CEMsFEM is applicable for practical engineering problems.

Free vibration analysis of a spinning piezoelectric beam with geometric nonlinearities

The linear and non-linear free vibrations of a spinning piezoelectric beam are studied by considering geometric nonlinearities and electromechanical coupling effect. The non-linear differential equations of the spinning piezoelectric beam governing two transverse vibrations are derived by using transformation of two Euler angles and the extended Hamilton principle, wherein an additional piezoelectric coupling term and different linear terms are present in contrast to the traditional shaft model. Linear frequencies are obtained by solving the standard eigenvalues of the linearized system directly, and the non-linear frequencies and non-linear complex modes are achieved by using the method of multiple scales. For free vibrations analysis of a spinning piezoelectric beam, the non-linear modal motions are investigated as forward and backward precession with different spinning speeds. The responses to the initial conditions for this gyroscopic system are studied and a beat phenomenon is found, which are then validated by numerical simulation. The influences of some parameters such as electrical resistance, rotary inertia and spinning speeds to the non-linear dynamics of a spinning piezoelectric beam are investigated.

An improved multiscale finite element method for nonlinear bending analysis of stiffened composite structures

SummaryStiffened composite structures are commonly composed of skins and stiffeners that are employed to transfer and carry load, respectively. An improved multiscale finite element method is presented for geometrically nonlinear bending analysis of composite grid stiffened laminates. In the developed method, two kinds of strategies for establishing stiffened multiscale models are presented, in which the stiffeners are modeled at different scale. By introducing a virtual degree of freedom and additional coupling terms, multiscale base functions are improved to consider the local effects of stiffeners and coupling effects of composites. To construct the multiscale base functions of stiffened multiscale models, an extended displacement boundary conditions are constructed, in which the displacements of stiffeners are imposed constraints based on the displacement continuous conditions between skin and stiffener. Incremental multiscale finite element formulations are derived based on Total‐Lagrange description and von Karman's large deflection plate theory. The incremental displacement boundary conditions are constructed to consider the effect of microscopic unbalanced force on microscopic results. Numerical examples show high efficiency and applicability of the developed method for composite grid stiffened laminates.

Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study

A generalized quantum Rabi Hamiltonian with both one- and two-photon terms has emerged in the circuit quantum electrodynamics system for a decade. The usual parity symmetry is broken naturally in the simultaneous presence of both couplings, which complicates analytical treatments, even in the rotating wave approximations. In this paper, we propose an adiabatic approximation to this generic model by using Bogoliubov operators, and obtain a very concise analytical solution for both eigenvalues and eigenstates. Although the adiabatic approximation is only exact in the vanishing limit of the qubit frequency, the results for some physical observables nevertheless agree well with the numerical ones in a wide parameter regime. In the rotating-wave approximations, we also derive an analytical eigensolution. Two dominant Rabi frequencies are found in the Rabi oscillations of this generalized model. We also apply the present analytical theory to the vacuum Rabi splitting. It is found that some new phenomena emerge just because of the presence of the additional two-photon coupling term.

Spin-selective electron transfer reactions of radical pairs: Beyond the Haberkorn master equation

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond the second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact hierarchical equations of motion method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.