Ordinary Theory Research Articles

Matrix ensembles with global symmetries and \u2019t Hooft anomalies from 2d gauge theory

The Hilbert space of a quantum system with internal global symmetry G decomposes into sectors labelled by irreducible representations of G. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such “sector-wise” random matrix ensembles arise as the boundary dual of two- dimensional gravity with a G gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of ’t Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with G symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal ℤ2 symmetry.

The Investigations to Improvement performance of Non-displacement pile at Southern part of Bandung area

In an ordinary theory mentioning that Bored pile type is non-displacement pile instead of driven pile as displacement type. To change the bored pile become displacement type, need an effort to displace surrounding soil in the vicinity of bored pile, the compaction of concrete during installation is one of the solution. During compaction, the soil displaced and excess pore water pressure increase, then by allowing pore water pressure to dissipate, the ground improvement is happening. The modelling of pile loading test (PLT) were carried out in various w/c ratio in ambient condition on first liquidity index (LI1), LI2 and LI3, The direct shear test (DST) of clay soil (at LI1, LI2 and LI3) and at combination of clay + cement mortar at various w/c ratio were also carried out to encourage and endorse the simulation work. The ground improvement occurs as a results of : 1. Chemical reaction between cement and clay, 2. Enlargement of slip surface diameter at the interface between soil – soil cement mix hardened, 3. Increasing effective stress as an effect of allowing pore water pressure dissipation after compaction. This stabilization produce increasing strength properties up to 75 % at the optimum w/c ratio 0,4. Based on this findings, it recommends to include the ground improvement effect to bored pile foundation.

The Existence and Stability Analysis of Periodic Solution of Izhikevich Model

In this paper, based on the Izhikevich model, a more realistic hybrid impulsive neuron model combining model with state-dependent impulsive effects is proposed. By means of the theory of impulsive semidynamic system, the Poincare section and the ordinary differential equation geometry theory, the properties of the equilibrium points and the sufficient conditions for the existence and stability of different order-1 or order-2 periodic solutions of the system are derived near the equilibrium point or limit cycle. In addition, subthreshold bifurcation behavior which are saddle-node bifurcation, Andronov-Hopf bifurcation, Bogdano-Takens bifurcation and bifurcation behavior of the model with state-dependent impulsive effects are also studied. Final, the main results are illustrated by numerical simulations, and the bifurcation diagram shows that the system becomes more complicated due to the existence of impulses, and there exist bifurcations and chaos phenomena, indicating that the system has rich dynamic behavior.

Transplanckian censorship and the local swampland distance conjecture

The swampland distance conjecture (SDC) addresses the ability of effective field theory to describe distant points in moduli space. It is natural to ask whether there is a local version of the SDC: is it possible to construct local excitations in an EFT that sample extreme regions of moduli space? In many cases such excitations exhibit horizons or instabilities, suggesting that there are bounds on the size and structure of field excitations that can be achieved in EFT. Static bubbles in ordinary Kaluza-Klein theory provide a simple class of examples: the KK radius goes to zero on a smooth surface, locally probing an in- finite distance point, and the bubbles are classically unstable against radial perturbations. However, it is also possible to stabilize KK bubbles at the classical level by adding flux. We study the impact of imposing the Weak Gravity Conjecture (WGC) on these solutions, finding that a rapid pair production instability arises in the presence of charged matter with q/m ≳ 1. We also analyze 4d electrically charged dilatonic black holes. Small curvature at the horizon imposes a bound log (MBH) ,≳ |∆\U0001d719|, independent of the WGC, and the bound can be strengthened if the particle satisfying the WGC is sufficiently light. We conjecture that quantum gravity in asymptotically flat space requires a general bound on large localized moduli space excursions of the form |∆\U0001d719| ≲ | log(RΛ)|, where R is the size of the minimal region enclosing the excitation and Λ−1 is the short-distance cutoff on local EFT. The bound is qualitatively saturated by the dilatonic black holes and Kaluza-Klein monopoles.

A New Classification of Hemirings through Double-Framed Soft h-Ideals

Due to lack of parameterization, various ordinary uncertainty theories like theory of fuzzy sets, and theory of probability cannot solve complicated problems of economics and engineering involving uncertainties. The aim of the present paper was to provide an appropriate mathematical tool for solving such type of complicated problems. For the said purpose, the notion of double-framed soft sets in hemirings is introduced. As h-ideals of hemirings play a central role in the structural theory, therefore, we developed a new type of subsystem of hemirings. Double-framed soft left (right) h-ideal, double-framed soft h-bi-ideals and double-framed soft h-quasi-ideals of hemiring are determined. These concepts are elaborated through suitable examples. Furthermore, we are bridging ordinary h-ideals and double-framed soft h-ideals of hemirings through double-framed soft including sets and characteristic double-framed soft functions. It is also shown that every double-framed soft h-quasi-ideal is double-framed soft h-bi-ideal but the converse inclusion does not hold. A well-known class of hemrings i.e. h-hemiregular hemirings is characterized by the properties of these newly developed double-framed soft h-ideals of

ε -regime of dilaton chiral perturbation theory

The $\epsilon$-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the $\epsilon$-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the $\epsilon$-regime and the $p$-regime. In the $\epsilon$-regime, moreover, all results agree with the universal predictions to leading order in $\epsilon$.

Plastic deformation due to high-velocity impact using ordinary state-based peridynamic theory

Peridynamic theory is a new and successful method to model the material behavior under impact loading. The bond-based peridynamic approach can be used to study the impact damage for brittle cases, but this method is unable to model the response of a ductile target due to plastic deformation of the structure. To capture the ductile fracture, the advanced class of this theory, called ordinary state-based peridynamic method, can be used. This approach has been previously utilized and described by literature to model the plastic deformation in some simple conditions. The present study aims to investigate the mentioned method to model the plastic deformation caused by high-velocity impact. For this purpose, the ductile behavior of a steel strip induced by high-velocity impact of various projectile shapes is considered. In this regard, the penetration process is studied at different impact velocities and magnitudes of strain hardening. The results show that the employed method can clearly capture the plastic behavior of the steel target and its “edge back” phenomenon. It confirms the ability of the utilized method to simulate the dynamic ductile fracture.

An ordinary state-based peridynamic modeling for dynamic fracture of laminated glass under low-velocity impact

Laminated glass, as a typical kind of sandwich-structure composite, is widely used in various fields such as safety, vehicle and transportation engineering. Laminated glass mainly suffers from dynamic/impact loadings, and glass-ply cracking is the main failure pattern of laminated glass. This paper presents a non-local ordinary state-based peridynamic modeling and numerical approach for simulating the dynamic failure process of sandwiched laminated glass under low-velocity impact loading. The mechanical behavior of the PVB layer is simulated by reformulating classical visco-elastic model under the framework of ordinary state-based peridynamic theory, and the adhesion between the glass and PVB interlayer is described by using a penalty-based method. Fracture patterns of a laminated glass plate under drop-weight loading were investigated, and the numerical results compared well with experimental observations. Furthermore, a series of numerical simulations were conducted to in-depth analyze the effect of the thickness of the PVB interlayer and the glass layers on the fracture mode, initial locations and crack propagation speed of the laminated glass when subjected to impact.

Dynamical correlations and pairwise theory for the symbiotic contact process on networks.

The two-species symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.

Equilibrium States in Thermal Field Theory and in Algebraic Quantum Field Theory

In this paper we compare the construction of equilibrium states at finite temperature for self-interacting massive scalar quantum field theories on Minkowski spacetime proposed by Fredenhagen and Lindner with results obtained in ordinary thermal field theory, by means of real time and Matsubara formalisms. In the construction of this state, even if the adiabatic limit is considered, the interaction Lagrangian is multiplied by a smooth time cut-off. In this way the interaction starts adiabatically and the correlation functions are free from divergences. The corresponding interaction Hamiltonian is a local interacting field smeared over the interval of time where the chosen cut-off is not constant. In order to cope with this smearing, the Matsubara propagator needs to be modified. We obtain an expansion of the correlation functions of the interacting equilibrium state as a sum over certain type of graphs with mixed edges, some of them correspond to modified Matsubara propagators and others to propagators of the real time formalism. An integration over the adiabatic time cut-off is present in every vertex. However, at every order in perturbation theory, the final result does not depend on the particular form of the cut-off function. The obtained graphical expansion contains in it both the real time formalism and the Matsubara formalism as particular cases. Finally, we show that a particular factorisation which is used to derive the ordinary real time formalism holds only in special cases and we present a counterexample. We conclude with the analysis of certain correlation functions and we notice that corrections to the self-energy in a $\lambda\phi^4$ at finite temperature theory are expected.

Non-Abelian basis tensor gauge theory

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.

Hall Conductivity as the Topological Invariant in the Phase Space in the Presence of Interactions and a Nonuniform Magnetic Field

The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently, the generalization of this expression has been proposed for the nonuniform magnetic field. The quantum Hall conductivity is represented as the topological invariant in phase space in terms of the Wigner transformed two-point Green’s function. This representation has been derived when the interelectron interactions were neglected. It is natural to suppose, that in the presence of interactions the Hall conductivity is still given by the same expression, in which the non-interacting Green’s function is substituted by the complete two-point Green’s function including the interaction contributions. We prove this conjecture within the framework of the 2 + 1 D tight-binding model of rather general type using the ordinary perturbation theory.

Probing non-Hermitian skin effect and non-Bloch phase transitions

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry breaking phase transitions in systems with open boundaries. Recently, it has been shown that a correct description requires to extend Bloch band theory into complex plane. A still open question is whether non-Hermitian skin effect and non-Bloch symmetry-breaking phase transitions can be probed by real-space wave dynamics far from edges, which is entirely governed by ordinary Bloch bands. Here it is shown that the Lyapunov exponent in the long-time behavior of bulk wave dynamics can reveal rather generally non-Bloch symmetry breaking phase transitions and the existence of the non-Hermitian skin effect.

Stringy (Galilei) Newton-Hooke Chern-Simons gravities

We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case there is no invariant non-degenerate bilinear form. Therefore, in both cases we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations we express the spin connections in terms of the geometric fields.

Why converting field emission voltages to macroscopic fields before making a Fowler-Nordheim plot has often led to spurious characterization results

An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γC. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an “orthodoxy test” allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the related papers were reporting spuriously high values for γC. In technological papers relating to LAFE characterization, the common practice is to preconvert the measured voltage into an (apparent) value of the macroscopic field before making and analyzing an FN plot. This paper suggests that the cause of the “spurious field enhancement factor value” problem is the widespread use of a preconversion equation that is defective (for example, not compatible with ordinary electrical circuit theory) when it is applied to so-called “nonideal” field emission devices/systems. Many real devices/systems are nonideal. The author argues that FN plots should be made using raw experimental current-voltage data, that an orthodoxy test should be applied to the resulting FN plot before any more-detailed analysis, and that (in view of growing concerns over the reliability of published “scientific” results) reviewers should scrutinize field emission materials characterization papers with enhanced care.

Tight binding approach for cuprate superconductors–Energy of the mean field and the correlation

We construct a mean field theory different from the wave vector representation, based on the observation that the ordinary mean field theory for superconductivity involves an inconsistency in the description of high Tcd-wave superconductivity. By using a cell- and ion-position (site position) representation, we obtain a basis for the tight-binding approximation (TBA) of the energy gap parameter and the energy of the pair condensate system. The mean field Hamiltonian is not diagonalized exactly by the Bogoliubov transformation, but a diagonalizable Hamiltonian may be defined by a truncation of that. A modified BCS model is introduced accompanying this Hamiltonian. We calculate the energy of the mean field and, moreover, the correlation energy of the condensate system in the TBA. We use the Gaussian orbital method to show that the gap parameter has a d-wave-like node structure in the form defined in the wave vector representation, but the gap in the site position representation and the quasiparticle energy do not have a node structure. The correction of the gap parameter by the off-site pair interaction is shown to be the first-order perturbation and the correction of the mean field energy is the second-order perturbation. The ratio of the correlation energy to the mean field energy is on the order of the carrier concentration in this TBA.

Test-field limit of metric nonlinear gravity theories

In the framework of alternative metric gravity theories, it has been shown by several authors that a generic Lagrangian depending on the Riemann tensor describes a theory with 8 degrees of freedom (which reduce to 3 for f(R) Lagrangians depending only on the curvature scalar). This result is often related to a reformulation of the fourth-order equations for the metric into a set of second-order equations for a multiplet of fields, including – besides the metric – a massive scalar field and a massive spin-2 field (the latter being usually regarded as a ghost): this is commonly assumed to represent the particle spectrum of the theory. In this article we investigate an issue which does not seem to have been addressed so far: in ordinary general-relativistic field theories, all fundamental fields (i.e. fields with definite spin and mass) reduce to test fields in some appropriate limit of the model, where they cease to act as sources for the metric curvature. In this limit, each of the fundamental fields can be excited from its ground state independently from the others (which does not happen, instead, as long as the fields are coupled through the gravitational interaction). We thus address the following question: does higher-derivative gravity admit a test-field limit for its fundamental fields? It is easy to show that for a generic f(R) theory (carrying 3 d.o.f.) the test-field limit does exist; then, we consider the case of Lagrangians depending on the full Ricci tensor, relying on a previous analysis published several years ago. We show that, already for a quadratic Lagrangian, the constraint binding together the scalar field and the massive spin-2 field does not disappear in the limit where they should be expected to act as test fields. A proper test-field limit exists only for a particular choice of the coefficients in the Lagrangian, which cause the scalar field to disappear (so that the resulting model has only 7 d.o.f.). We finally consider the possible addition of an arbitrary function of the quadratic invariant of the Weyl tensor, C^{alpha }{}_{beta mu nu }C_{alpha }{}^{beta mu nu }, showing that the appearance of the Weyl tensor does not add physical degrees of freedom (in accordance to the known results for Lagrangians depending on the full Riemann tensor) and the resulting model with 8 d.o.f. still lacks a proper test-field limit: the differential constraints between the fundamental fields do not cancel out when gravitational interaction is suppressed. We argue that the lack of a test-field limit for the dynamics of the fundamental fields may constitute a serious drawback of the full 8 d.o.f. higher-order gravity models, which is not encountered in the restricted 7 d.o.f. or 3 d.o.f. cases.

The third Sandia Fracture Challenge: peridynamic blind prediction of ductile fracture characterization in additively manufactured metal

In the context of the third Sandia Fracture Challenge (SFC3), the details of the blind predictions performed by the University of Texas team are provided in this article. Over the past two decades, the peridynamic theory has shown great promise in modeling autonomous crack nucleation and growth in materials. While peridynamics has been commonly applied to simulate failure of brittle materials, its ability in predicting ductile fracture has remained mostly untested. This fracture challenge was seen as an opportunity to assess the state of the art of the peridynamic theory in predicting the response of an additively manufactured 316L stainless steel bar with a complex geometry under the dynamic tensile experiments performed by Sandia National Laboratories. The performance of a recently proposed, generalized, ordinary finite deformation constitutive correspondence model, coupled with a recent state-based damage correspondence model was explored over this problem. For finite deformation material modeling, the classical elastoplastic framework of Simo was implemented within the ordinary correspondence theory. Damage modeling was achieved by incorporating the Johnson-Cook failure criterion using the damage correspondence framework. An iterative inverse technique was applied to calibrate the model parameters using the longitudinal and notched tensile tests data provided by Sandia National Laboratories. A blind prediction of the deformation and failure behavior of the SFC3 geometry was performed by embedding the calibrated model in a peridynamic simulation. Uncertainty was introduced into the model parameters to quantify material variability. The results are compared to the experiments conducted at Sandia National Laboratories. While our modeling approach led to qualitatively good results and a correctly predicted crack path, it underpredicted the load-carrying capacity of the structure and simulated an early fracture. Our post-experiment analysis identifies material instability issues associated with the model as the primary sources of error.

Non-perturbative quantum chromodynamics and short strings in electron-positron pair annihilation to hadrons

We develop a new mathematical method to study the non-perturbative quantum chromodynamics effects in low-energy processes using ordinary and analytic perturbation theory (PT and APT). We apply this tool to extract the lowest dimensional condensates from the high-precision fits of the data on e+e–-annihilation to pion channels:  e+e− → π+π−, e+e− → 2π+2π−, e+e− → π+π−2π0, e+e− → 3π+3π− and e+e− → 2π+2π−2π0. The special attention is devoted to the existence of the contribution of dimension 2 operator. Our consideration is based on the dependence of Adler function corresponding to e+e−-annihilation into pions on both Q and Borel transform parameter M2. It is shown that within the framework of the proposed method the C2 coefficient of the dimension 2 operator is negative and is closer to zero for analytic perturbation theory, which may therefore be partially responsible for the effect of short strings.

Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model

We present the results of an exploratory study of the numerical stochastic perturbation theory (NSPT) applied to the four dimensional twisted Eguchi-Kawai (TEK) model. We employ a Kramers type algorithm based on the Generalized Hybrid Molecular Dynamics (GHMD) algorithm. We have computed the perturbative expansion of square Wilson loops up to O(g8). The results of the first two coefficients (up to O(g4)) have a high precision and match well with the exact values. The next two coefficients can be determined and even extrapolated to large N, where they should coincide with the corresponding coefficients for ordinary Yang-Mills theory on an infinite lattice. Our analysis shows the behaviour of the probability distribution for each coefficient tending to Gaussian for larger N. The results allow us to establish the requirements to extend this analysis to much higher order.