Auxiliary Field Research Articles

Computation of two dimensional mixed-mode stress intensity factor rates using a complex-variable interaction integral

The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack extensions for an isotropic linear elastic material under static loading. These derivatives were calculated using the complex Taylor series expansion (CTSE) numerical differentiation method. The derivatives of the auxiliary fields are calculated by applying CTSE directly to the M-integral formulation. The derivatives of the actual displacement fields are computed using a hypercomplex-variable finite element method (ZFEM) that also employs CTSE. SIF rates with respect to all crack tips are computed in a single analysis. The method is general and can be easily extended to other two-dimensional loading scenarios and different material models in a straightforward manner through the use of the appropriate auxiliary fields. The complex-variable M-integral was implemented within the commercial finite element software Abaqus through a user-defined element subroutine (UEL). Numerical examples demonstrate the high accuracy of the method.

Field Form of the Dynamics of Classical Many- and Few-Body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics

A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It is established that for interatomic potentials, the Fourier transform of which is a rational algebraic function of the wave vector, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and a non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established.

Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions

We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.

Magnetic domain wall motion driven by spin-orbit torque based on non-collinear spin source

<p indent="0mm">Recently, the current-induced motion of magnetic domain walls has attracted much attention. It enables electrical control of domain wall motion without the application of an external magnetic field and thus has potential applications in high-performance magnetic racetrack memories, among others. The effective control of domain wall motion under zero magnetic field is one of the important topics in spintronics research. Current-driven magnetization switching via the spin-orbit torque effect is an important approach to realizing the field-free domain wall motion. The traditional research structure of spin-orbit torques is non-magnetic material/magnetic material (NM/FM) heterogeneous films, in which non-magnetic materials are used as the spin source layer to generate and provide spin current through charge-to-spin current conversion. Common non-magnetic materials mainly include heavy metals, such as Pt, β-Ta and β-W. However, in the system with heavy metals as spin sources, the conventional spin Hall effect requires the charge current, spin current and spin polarization directions to be perpendicular to each other, so it is necessary to apply an in-plane auxiliary magnetic field to break the symmetry, especially when driving the perpendicular magnetic moment switching, which increases extra power consumption and is not conducive to practical applications. Recently, it has been found that the spin current generated by the charge current in the outer semimetal WTe₂ is spin polarized in the <bold><italic>z</italic></bold>-direction. It has a unique in-plane symmetry breaking property, where the damping-like torque can contribute more to the domain wall motion of a ferromagnetic layer with perpendicular magnetic anisotropy. Moreover, a unique Rashba-like spin polarization has recently emerged in the noncollinear magnetic structure Mn₃GaN. A charge current is applied in the <bold><italic>x</italic></bold>-direction to generate a spin current in the <bold><italic>z</italic></bold>-direction, with spin polarization along the <bold><italic>x</italic></bold>-direction. The spin polarization along the <bold><italic>x</italic></bold>-direction produces damping-like torque (<bold><italic>τ</italic></bold>_{<italic>x</italic>}_,DL) and field-like torque (<bold><italic>τ</italic></bold>_{<italic>x</italic>}_,FL) in the adjacent in-plane and PMA ferromagnetic layers. The magnetization dynamics of the SOT mentioned above may be quite different. To realize the effectively current-induced spin-orbit torque driven domain wall motion, it is important to understand the spin source with unique physical properties of charge-to-spin conversion. In this work, we study the spin-orbit torque driven domain wall motion by micromagnetic simulations. We consider the mixture of non-collinear spin torques of Rashba-like <bold><italic>S</italic></bold><italic>_y</italic>, Dresselhaus-like <bold><italic>S</italic></bold><italic>_x</italic>, and out-of-plane <bold><italic>S</italic></bold><italic>_z</italic>. The effects of three different domain wall types: Bloch domain wall, Néel domain wall and head-to-head domain wall on motion velocity and the inclination angles of magnetic domain walls are demonstrated. The results for the same magnetic domain show that the current-induced spin polarization perpendicular to the membrane surface generates a damping-like torque perpendicular to the membrane surface, which can efficiently drive the motion of the domain wall. However, in the presence of multiple spin torques, the unconventional damping-like torques in the direction perpendicular to the film surface can be realized to drive domain wall motion at zero field. Our results may provide a new degree of freedom for understanding current-induced spin-orbit torque-driven domain wall motion from non-collinear spin sources for potential applications in spintronic devices.

Interaction integral approach for the Evaluation of Crack-front Singularities in a Solid Cantilever Beam under Magneto-Electro-Elastic loading using XFEM

In the piezoelectric energy harvesting devices, the most preferred is the cantilever beam orientation that can produce maximum deflection. Therefore, in this paper, three-dimensional fracture analysis of a cracked magneto-electro-elastic cantilever beam is studied using extended finite element methods (XFEM). The crack-front singularities like stress intensity factors (SIFs), electric displacement intensity factor (EDIF), and magnetic induction intensity factor (MIIF) are evaluated using the MEE interaction integral approach. The contour J-integral in domain form is solved with the asymptotic crack front fields as auxiliary fields using the Stroh formalism. The numerical results showed good agreement with the benchmark problem. Few case studies for the crack front singularities are presented using the proposed method. The results provided give useful guidance in the designing and manufacturing of smart devices.

Electrospun aligned nanofibers: A review

Electrospinning (e-spinning) is famous for the construction and production of ultrafine and continuous micro-/nanofibers. Then, the alignment of electrospun (e-spun) nanofibers becomes one of the most valuable research topics. Because aligned fibers have more advantages over random fibers, such as better mechanical properties, faster charge transport, more regular spatial structure, etc. This review summarizes various electrospinning techniques of fabricating aligned e-spun nanofibers, such as early conventional methods, near-field e-spinning, and three-dimensional (3D) printing e-spinning. Among them, four auxiliary preparation methods (e.g., auxiliary solid template, auxiliary liquid, auxiliary electromagnetic field and auxiliary airflow), two collection modes (static and dynamic collection), and the controllability of near-field e-spinning and 3D printing e-spinning are highlighted. The representative applications depending on aligned nanofibers are classified and briefly introduced, emphasizing in the fields of 1D applications (e.g., field-effect transistor, nanochannel and guidance carrier), 2D applications (e.g., platform for gas detection, filter, and electrode materials storage), and 3D applications (e.g., bioengineering, supercapacitor, and nanogenerator). At last, the challenges and prospects are addressed.

Role of Auxiliary Potentials and Fields in the Shockley–Ramo Theorem for Inhomogeneous Locally Anisotropic Samples with Polarization

Role of Auxiliary Potentials and Fields in the Shockley–Ramo Theorem for Inhomogeneous Locally Anisotropic Samples with Polarization

Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study

We show that for the half-filled Kondo lattice model on the honeycomb lattice a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo simulations of the so-called composite fermion spectral function. Within a U(1) gauge theory formulation of the Kondo model, it becomes apparent that a Higgs mechanism dictates the weight of the resonance in the spectral function. For the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole gives way to incoherent spectral weight but it remains well defined for the square lattice. Our result provides an explicit example where the magnetic transition and the breakdown of heavy quasiparticles are detached as observed in Yb(Rh$_{0.93}$Co$_{0.07}$)$_2$Si$_2$ [Friedemann et al., Nat. Phys. \textbf{5}, 465 (2009)].

Improved microstructure and performance of thick-walled 316L stainless steel joint by NG-GTAW with auxiliary magnetic field

Thick-walled 316L stainless steel (SS) was successfully welded by magnetic field assisted arc oscillation narrow gap GTAW (gas tungsten arc welding). The microstructure and weld performance of thick-walled 316 SS joints with and without arc oscillation were reported. The results indicated that the solute segregation of 316L SS welded joints was improved, ferrite content was significantly reduced, and the overall grain size was also refined under the action of arc oscillation, which may be mainly attributed to the uniform temperature and the reduced cooling rate resulting from the application of magnetic field. Furthermore, the growth direction of the columnar grain in the weld was changed and the texture characteristic of the grain was weakened with arc oscillation. Consequently, the strength and plasticity of the weld were improved synergistically. Based on the SEM and EBSD analysis, the enhanced corrosion resistance of selected position in the joint also was evaluated by weighing the solute segregation, phase proportion and grain boundary characteristic.

Path-integral quantum Monte Carlo calculations of light nuclei

We describe a path-integral ground-state quantum Monte Carlo method for light nuclei in continuous space. We show how to efficiently update and sample the paths with spin-isospin dependent and spin-orbit interactions. We apply the method to the triton and alpha particle using both local chiral interactions with next-to-next-to-leading-order %(N$^2$LO) and the Argonne interactions. For operators, like the total energy, that commute with the Hamiltonian, our results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo calculations. For operators that do not commute with the Hamiltonian and for Euclidean response functions, the path-integral formulation allows straightforward calculation without forward walking or the increased variance typical of diffusion methods. We demonstrate this by calculating density distributions, root mean square radii, and Euclidean response functions for single-nucleon couplings.

Weyl double copy and massless free-fields in curved spacetimes

In spinor formalism, since any massless free-field spinor with spin higher than 1/2 can be constructed with spin-1/2 spinors (Dirac–Weyl (DW) spinors) and scalars, we introduce a map between Weyl fields and DW fields. We determine the corresponding DW spinors in a given empty spacetime. Regarding them as basic units, other higher spin massless free-field spinors are then identified. Along this way, we find some hidden fundamental features related to these fields. In particular, for non-twisting vacuum Petrov type N solutions, we show that all higher spin massless free-field spinors can be constructed with one type of DW spinor and the zeroth copy. Furthermore, we systematically rebuild the Weyl double copy for non-twisting vacuum type N and vacuum type D solutions. Moreover, we show that the zeroth copy not only connects the gravity fields with a single copy but also connects the degenerate Maxwell fields with the DW fields in the curved spacetime, both for type N and type D cases. Besides, we extend the study to non-twisting vacuum type III solutions. We find a particular DW scalar independent of the proposed map and whose square is proportional to the Weyl scalar. A degenerate Maxwell field and an auxiliary scalar field are then identified. Both of them play similar roles as the Weyl double copy. The result further inspires us that there is a deep connection between gravity theory and gauge theory.

Optimization of blocked flow field performance of proton exchange membrane fuel cell with auxiliary channels

The flow field optimization design is one of the important methods to improve the performance of proton exchange membrane fuel cell (PEMFC). In this study, a new structure with staggered blocks on the parallel flow channels of PEMFC and auxiliary flow channels under the ribs is proposed. Through numerical calculation method, the effect of blocks auxiliary flow field (BAFF) on pressure drop, reactant distribution and liquid water removal in the fuel cells are investigated. The results show that when the operating voltage is 0.5 V, the current density of BAFF is 21.74% higher than that of the straight parallel flow field (SPFF), and the power density reaches 0.65 W cm−2. BAFF improves performance by equalizing the pressure drop across sub-channels, promoting the uniform distribution of reactant, and enhancing transport across the ribs. In addition, through parameter analysis, it is found that BAFF can discharge liquid water in time at the conditions of high humidification, high current density and low temperature, which ensures the output performance of the fuel cell and improves the durability of the fuel cell. This paper provides new ideas for the improvement of PEMFC flow field design, which is beneficial to the development of PEMFC with high current density.

Negative sign free formulations of generalized Kitaev models with higher symmetries

We provide a negative-sign-free formulation of the auxiliary field quantum Monte Carlo algorithm for generalized Kitaev models with higher symmetries. Our formulation is based on the Abrikosov fermion representation of the spin-1/2 degree of freedom and the phase pinning approach [Phys. Rev. B 104, L081106 (2021)]. Enhancing the number of fermion flavors or orbitals from one to $N$ allows one to generalize the inherent $Z_2$ global symmetry to Z$_2$$\times$SU($N$)$_o$. Using this general approach, we study the Z$_2$$\times$SU(2)$_o$ Kitaev-Heisenberg model reflecting the competition between the isotropic Heisenberg exchange and Kitaev-type bond-directional exchange interactions. We show that the symmetry enhancement provides a path to escape frustration and that the spin liquid phases in the original Z$_2$ symmetric model are not present in this model. Nevertheless, the ground-state phase diagram is extremely rich and has points with higher global and local continuous symmetries as well as de-confined quantum critical points.

A note on higher rank descriptions of massless and massive spin-1 particles

The Maxwell theory can be written as a first order model with the help of a two-form auxiliary field, such master action allows the proof of duality between 1-form and D−3 forms. Here we show that the replacement of the two-form auxiliary field by an arbitrary (non symmetric) rank-2 tensor leads to a new massless spin-1 dual theory in terms of a partially antisymmetric rank-3 tensor. In the massive spin-1 case we have a non symmetric generalization of the massive two-form theory (Kalb–Ramond). The coupling of the massive non symmetric spin-1 model to matter fields is investigated via master actions.We also show that massive models with severe discontinuity in their massless limit can also be obtained from Kaluza–Klein dimensional reduction of massless higher rank tensors which become Stueckelberg fields after the reduction.

Body-of-revolution finite-difference time-domain modeling of hybrid-plasmonic ring resonators.

Development of a computational technique for the analysis of quasi-normal modes in hybrid-plasmonic resonators is the main goal of this research. Because of the significant computational costs of this analysis, one has to take various symmetries of these resonators into account. In this research, we consider cylindrical symmetry of hybrid-plasmonic ring resonators and implement a body-of-revolution finite-difference time-domain (BOR-FDTD) technique to analyze these resonators. We extend the BOR-FDTD method by proposing two different sets of auxiliary fields to implement multi-term Drude-Lorentz and multi-term Lorentz models in BOR-FDTD. Moreover, we utilize the filter-diagonalization method to accurately compute the complex resonant frequencies of the resonators. This approach improves numerical accuracy and computational time compared to the Fourier transform method used in previous BOR-FDTD methods. Our numerical analysis is verified by a 2D axisymmetric solver in COMSOL Multiphysics.

2D Electron System with Quasiparticle Auxiliary Field Correlation of Open quantum System

The objective of this work is to develop the mathematical model for the auxiliary field and interlink the pair correlation in the external potential of the open quantum system of the 2D electron system. For this, we used 2D Hubbard Model with the action open quantum system Lindblad equation and then apply the saddle point condition to obtain the auxiliary field of the 2D system. The obtained pair correlation of quasiparticles was found symmetric in nature with cooper pairs electron paring angle. The pair correlation of 0K was found 0.1times, 1 time, 2 times, 3 times, 4 times, and 5 times greater when compared with 0.2K, 0.3K, 0.4K, 0.5K, and 0.6K, respectively at -1 radian and +1 radian copper pairs electron pairing angle which is maximum. In addition, with increasing the temperature, the pair correlation decrease and become minimum without loss of symmetry.

The Casimir effect in chiral media using path integral techniques

We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background θ field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of configurations, and where comparison is possible our results are in perfect agreement with existing literature. Among these are multiple situations where a repulsive Casimir force is possible.

Modified geodesic equations of motion for compact bodies in alternative theories gravity

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating the effects of self-gravity within gravitationally bound bodies, in which their masses may depend on invariant quantities constructed from the auxiliary scalar, vector or tensor fields introduced by such theories, evaluated in the vicinity of each body. The forms of the equations are independent of the field equations of the chosen theory. In the case where the masses are strictly constant, the equations reduce to the conventional geodesic equations of general relativity. These equations may be useful tools for deriving equations of motion for compact bodies to high post-Newtonian orders in alternative theories of gravity.

Multi-kink braneworld configurations in the scalar-tensor representation of f(R, T) gravity

In this work we investigate the $f(R,T)$ brane in the scalar-tensor representation, where the solutions of the equations of motions for the source field engender topological defects with two-kink profiles. We use the first-order formalism to obtain analytical solutions for the source field of the brane and analyze how these solutions modify the structure of the auxiliary fields arising from the scalar-tensor representation of the theory. We found that when the model engenders two-kink solutions, the auxiliary fields are modified in order to allow for the appearance of an internal structure. In addition, the stability potential and zero mode also have their internal structure modified by two-kink solution.

Influence of transverse auxiliary magnetic field on weld formation and joint quality in spiral submerged arc welding of X80 steel linepipe

Influence of transverse auxiliary magnetic field on weld formation and joint quality in spiral submerged arc welding of X80 steel linepipe