Particular Set Of Boundary Conditions Research Articles

Time-harmonic analysis of acoustic pulsation in gas pipeline systems using the Finite Element Transfer Matrix Method: Theoretical aspects

Structural vibration of gas pipeline systems can be strongly affected by the response of the acoustic domain represented by the gas being transported through pressurized pipes, cylinders and other related components. The resultant Acoustically Induced Vibration (AIV) can be a cause of failure, for example, in reciprocating compressor systems, where the discharge and suction pulsations are the main source of excitation. The objective of this work is to explore and enhance the use of the Finite Element Transfer Matrix Method (FETM) for solving time-harmonic acoustic problems related to AIV, whose results can be used to analyze pulsation in piping systems. Four different damping models are explored and implemented (apart from the classical undamped model) resulting in five different acoustic elements for the quiescent fluid case. In addition, two different damping models are analyzed for the case of a fluid with mean flow, and implemented through two flow-acoustic elements. The physical behavior of certain typical junctions is also investigated, represented by acoustic and flow-acoustic length corrections, and an FETM formulation is proposed to account for local non-linear effects in transfer impedance elements. Also, a discussion related to the minimum and maximum FETM element sizes is presented. A critical analysis of the effectiveness of the whole FETM strategy is performed using a variety of representative gas pipeline geometries as application examples with a particular set of boundary conditions for quiescent and moving fluid medium. Nodal pressure frequency plots of cases considering all the presented acoustic and flow-acoustic elements, and related damping models, are presented. Coherent results were achieved using the procedure when frequency plots are compared with experimental data and 3D FEM equivalent models.

Lifshitz scaling, microstate counting from number theory and black hole entropy

Non-relativistic field theories with anisotropic scale invariance in (1+1)-d are typically characterized by a dispersion relation E ∼ kz and dynamical exponent z > 1. The asymptotic growth of the number of states of these theories can be described by an extension of Cardy formula that depends on z. We show that this result can be recovered by counting the partitions of an integer into z-th powers, as proposed by Hardy and Ramanujan a century ago. This gives a novel duality relationship between the characteristic energy of the dispersion relation with the cylinder radius and the ground state energy. For free bosons with Lifshitz scaling, this relationship is shown to be identically fulfilled by virtue of the reflection property of the Riemann ζ-function. The quantum Benjamin-Ono2 (BO2) integrable system, relevant in the AGT correspondence, is also analyzed. As a holographic realization, we provide a special set of boundary conditions for which the reduced phase space of Einstein gravity with a couple of U (1) fields on AdS3 is described by the BO2 equations. This suggests that the phase space can be quantized in terms of quantum BO2 states. Indeed, in the semiclassical limit, the ground state energy of BO2 coincides with the energy of global AdS3, and the Bekenstein-Hawking entropy for BTZ black holes is recovered from the anisotropic extension of Cardy formula.

Parameters for the Collapse of Turbulence in the Stratified Plane Couette Flow

Abstract We perform direct numerical simulation of the Couette flow as a model for the stable boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux. First, we establish what the similarities and differences are between applying a fixed buoyancy difference (Dirichlet) and a fixed buoyancy flux (Neumann) as boundary conditions. Moreover, two distinct parameters were recently proposed for the turbulent-to-laminar transition: the Reynolds number based on the Obukhov length and the “shear capacity,” a velocity-scale ratio based on the buoyancy flux maximum. We study how these parameters relate to each other and to the atmospheric boundary layer. The results show that in a weakly stratified equilibrium state, the flow statistics are virtually the same between the different types of boundary conditions. However, at stronger stratification and, more generally, in nonequilibrium conditions, the flow statistics do depend on the type of boundary condition imposed. In the case of Neumann boundary conditions, a clear sensitivity to the initial stratification strength is observed because of the existence of multiple equilibriums, while for Dirichlet boundary conditions, only one statistically steady turbulent equilibrium exists for a particular set of boundary conditions. As in previous studies, we find that when the imposed surface flux is larger than the maximum buoyancy flux, no turbulent steady state occurs. Analytical investigation and simulation data indicate that this maximum buoyancy flux converges for increasing Reynolds numbers, which suggests a possible extrapolation to the atmospheric case.

Structure Preserving Finite Differences in Polar Coordinates for Heat and Wave Equations.

This paper proposes a finite difference spatial discretization that preserves the geometrical structure, i.e. the Dirac structure, underlying 2D heat and wave equations in cylindrical coordinates. These equations are shown to rely on Dirac structures for a particular set of boundary conditions. The discretization is completed with time integration based on Stormer-Verlet method.

Structural stability, asymptotic stability and exponential stability for linear multidimensional systems: the good, the bad and the ugly

ABSTRACTIn this paper, we investigate three concepts of stability for linear two-dimensional systems: the ‘good’ structural stability (an algebraic property linked to the location of the roots of a certain characteristic polynomial), the ‘bad’ asymptotic stability (roughly the trajectory converges to the equilibrium point) and the ‘ugly’ exponential stability (the rate of convergence is at least exponential). More precisely, we show that for a usual set of boundary conditions taken along the positive semi-axes, structural stability and exponential stability are equivalent notions. For this particular set of boundary conditions, we further prove that structural stability implies asymptotic stability but a counterexample shows that asymptotic stability does not imply structural stability which is a major difference compared to the one-dimensional case. This also highlights the importance of the boundary conditions when one works with multidimensional systems.

Aharonov-Bohm effect in graphene Möbius strips: an analytical treatment

In this work, the influence of an Aharonov-Bohm flux on the low energy physical properties of graphene nanorings exhibiting Mobius topology is examined. Our approach lies in the continuum description of graphene, providing an analytical treatment for Aharonov-Bohm problem in the context of general relativistic confined systems, whose main goal is to understand the role of boundary conditions and their effects in such a background. We study a class of quantum rings described by a particular set of boundary conditions which combines infinite mass confinement along the transverse direction with a Mobius-type periodicity longitudinally, in order to sketch out insights into the electronic behavior of typical hard wall nanoribbons within a relativistic domain in response to the interplay between non-trivial topology and quantum interference effects. Boundary conditions are found to be only partially compatible, leading to spatial constraints on the solution, which also manifests itself in the nature of energy spectrum and persistent currents. Expressions for flux-dependent energy eigenvalues and persistent currents are explicitly calculated, as well as comparative graphs are plotted and analyzed. Both quantities are shown to alternate their expressions not only in dependence on the transverse modes, but also showing sensitivity to the allowed positions of the domain.

Asymptotic structure of the Einstein-Maxwell theory on AdS3

The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to $\mathbb{R}\otimes U\left(1\right)\otimes U\left(1\right)$. Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and $U\left(1\right)$. This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.

Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory

In this study, the analytical solution of inter- laminar stresses near the free edges of a general (symmetric and unsymmetric layups) cross-ply composite laminate subjected to pure bending loading is presented based on Reddy's layerwise theory (LWT) for the first time. First, the reduced form of displacement field is obtained for a general cross-ply composite laminate subjected to a bend- ing moment by elasticity theory. Then, first-order shear deformation theory of plates and LWT is utilized to determine the global and local deformation parameters appearing in the displacement fields, respectively. One of the main advantages of the developed solution based on the LWT is exact prediction of interlaminar stresses at the boundary layer regions. To show the accuracy of this solution, three-dimensional elasticity bending problem of a laminated composite is solved for special set of boundary conditions as well. Finally, LWT results are presented for edge-effect problems of several symmetric and unsym- metric cross-ply laminates under the bending moment. The obtained results indicate high stress gradients of interlam- inar stresses near the edges of laminates.

Neutron stars in the Starobinsky model

We study the structure of neutron stars in $f(R)=R+\alpha R^{2}$ theory of gravity (Starobinsky model), in an exact and non-perturbative approach. In this model, apart from the standard General Relativistic junction conditions, two extra conditions, namely the continuity of the curvature scalar and its first derivative needs to be satisfied. For an exterior Schwarzschild solution, the curvature scalar and its derivative has to be zero at the stellar surface. We show that for some equation of state (EoS) of matter, matching all conditions at the surface of the star is impossible. Hence the model brings two major fine-tuning problems: (i) only some particular classes of EoS are consistent with Schwarzschild at the surface and (ii) given that EoS, only a very particular set of boundary conditions at the centre of the star will satisfy the given boundary conditions at the surface. Hence we show that this model (and subsequently many other f(R) models where uniqueness theorem is valid) is highly unnatural, for the existence of compact astrophysical objects. This is because the EoS of a compact star should be completely determined by the physics of nuclear matter at high density and not the theory of gravity.

Yukawa Unification Predictions with Effective “Mirage” Mediation

In this Letter we analyze the consequences, for the LHC, of gauge and third family Yukawa coupling unification with a particular set of boundary conditions defined at the grand unified theory (GUT) scale, which we characterize as effective "mirage" mediation. We perform a global χ2 analysis including the observables M(W), M(Z), G(F), α(em)(-1), α(s)(M(Z)), M(t), m(b)(m(b)), M(τ), BR(B→X(s)γ), BR(B(s)→μ(+)μ(-)), and M(h). The fit is performed in the minimal supersymmetric standard model in terms of 10 GUT scale parameters, while tanβ and μ are fixed at the weak scale. We find good fits to the low energy data and a supersymmetry spectrum which is dramatically different than previously studied in the context of Yukawa unification.

Yukawa unification predictions for the LHC

This paper is divided into two parts. In the first part we analyze the consequences, for the LHC, of gauge and third-family Yukawa coupling unification with a particular set of boundary conditions defined at the grand unification scale. We perform a global ${\ensuremath{\chi}}^{2}$ analysis including the observables ${M}_{W}$, ${M}_{Z}$, ${G}_{F}$, ${\ensuremath{\alpha}}_{\mathrm{em}}^{\ensuremath{-}1}$, ${\ensuremath{\alpha}}_{s}({M}_{Z})$, ${M}_{t}$, ${m}_{b}({m}_{b})$, ${M}_{\ensuremath{\tau}}$, $\mathrm{BR}(B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma})$, $\mathrm{BR}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$, and ${M}_{h}$. The fit is performed in the minimal supersymmetric Standard Model in terms of nine grand unification-scale parameters, while $\mathrm{tan}\ensuremath{\beta}$ and $\ensuremath{\mu}$ are fixed at the weak scale. Good fits suggest an upper bound on the gluino mass, ${M}_{\stackrel{\texttildelow{}}{g}}\ensuremath{\lesssim}2\text{ }\text{ }\mathrm{TeV}$. This constraint comes predominantly from fitting the bottom-quark and Higgs masses (assuming a 125 GeV Higgs). Gluinos should be visible at the LHC in the 14 TeV run but they cannot be described by the typical simplified models. This is because the branching ratios for $\stackrel{\texttildelow{}}{g}\ensuremath{\rightarrow}t\overline{t}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{0}$, $b\overline{b}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{0}$, $t\overline{b}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{\ensuremath{-}}$, $b\overline{t}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{+}$, $g{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2,3,4}^{0}$ are comparable. Top squarks and sbottoms may also be visible. Charginos and neutralinos can be light, with the lightest supersymmetric particle predominantly bino-like. In the second part of the paper we analyze a complete three-family model and discuss the quality of the global ${\ensuremath{\chi}}^{2}$ fits and the differences between the third-family analysis and the full three-family analysis for overlapping observables. We note that the light Higgs in our model couples to matter like the Standard Model Higgs. Any deviation from this would rule out this model.

Buckling of cross-ply laminates subject to linearly varying compressive loads and in-plane boundary restraints

In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary being restrained from deformation in the plane of the plate. These stresses exhibit a uniform distribution only under a special set of boundary conditions and in general such uniform in-plane stress distributions do not exist under most boundary conditions encountered in practice. In the present study, in-plane prebuckling stresses are investigated for various in-plane boundary constraints and the stress contour lines are given for rectangular cross-ply laminated plates under linearly varying edge loads. The second part of the article involves the computation of the optimal layer thickness to maximize the buckling load under various combinations of in-plane boundary restraints. The numerical solutions are obtained by finite elements based on first-order shear deformable plate theory which include the in-plane deformations as nodal degrees of freedom. Numerical results show that the exclusion of the in-plane restraints may lead to errors in stability calculations and consequently in the design of laminated plates.

Electrostatic field management and electrodynamic modeling of switched quarter-wave oscillators

Quarter-wave switched oscillators (SWOs), sometimes referred to as MATRIX oscillators, are an important technology for the generation of high-power, moderate bandwidth (mesoband) waveforms. The use of SWOs in high power microwave sources has been discussed for the past 10 years but a detailed discussion of the design of this type of oscillators for particular waveforms has been lacking. In this work a design methodology for a realization of SWOs is developed. A key element in the design of SWOs is the self-breakdown switch, which is created by a large electric field. In order for the switch to close as expected from the design, it is essential to manage the electrostatic field distribution inside the oscillator during the charging time. This enforces geometric constraints on the shape of the conductors inside the oscillator. At the same time, the electrodynamic operation of the system is dependent on the geometry of the structure. In order to generate a geometry that satisfies both the electrostatic and electrodynamic constraints, a new approach is developed to generate this geometry using iterative solutions to the 2-D static Laplace equation, subject to a particular set of boundary conditions. These boundary conditions are manipulated to generate equipotential lines with specific dimensions that satisfy the electrodynamic constraints. Meanwhile, these equipotential lines naturally support an electrostatic field distribution that meets the requirements for the field enhancement. To study the electrodynamic aspects of SWOs, three different (but inter-related) numerical models are built. Depending on the assumptions made in each model, different information about the electrodynamic properties of the designed SWO are obtained. In addition, the agreement and consistency between the different models, validate and give confidence in the calculated results.

Model-Based Monitoring and Leak Detection in Oil and Gas Pipelines

Summary An adaptive Luenberger-type estimator for the purpose of monitoring flow conditions and locating and quantifying leakages in petroleum pipelines is presented. The estimator only needs measurements of velocity, pressure, and temperature at the inlet and velocity and pressure at the outlet to function. The measurements are used to form a special set of boundary conditions for the estimator that ensures fast convergence of the estimation error. Depending only on measurements from inlet and outlet makes it possible to use OLGA, which is a state-of-the-art computational fluid dynamics simulator, to govern the one-phase fluid flow of the estimator. The estimator is tested with both a straight, horizontal pipeline and an actual, long pipeline with inclinations, and both simulations with oil and gas are carried out. In order to cope with modeling errors and biased measurements, estimation of roughness in the monitored pipeline is introduced.

Numerical methods for analysis of structure and ground vibration from moving loads

An overview of the main theoretical aspects of finite-element and boundary-element modelling of the response to moving loads is given. The moving loads represent sources of noise and vibration generated by moving vehicles, and the analysis describes the propagation of the disturbances generated in soil. A finite-element time-domain analysis in convected coordinates with a simple upwind scheme is presented, including a special set of boundary conditions permitting the passage of outgoing waves in the convected coordinate system. The modification of frequency-dependent damping to convected coordinates is described, and the convected formulation of boundary elements is presented and used for illustrating the effect of ‘high-speed’ motion. Finally, a procedure for the coupling of a local finite-element model with a boundary-element model of an exterior, or open, domain is described. The paper uses recent results from the Danish research programme ‘Damping Mechanisms in Dynamics of Structures and Materials’ as a basis for a general discussion and review of the recent literature on the subject.

Interlaminar stresses in antisymmetric angle-ply laminates

Based on elasticity theory the reduced form of displacement field is developed for long antisymmertic angle-ply composite laminates subjected to extensional and/or torsional loads. Analytical solutions to the edge-effect problem of such laminates under a uniform axial strain are developed using the first-order shear deformation theory of plates and Reddy’s layerwise theory. For a special set of boundary conditions an elasticity solution is presented to verify the validity and accuracy of the layerwise theory. Various numerical results are then developed within the layerwise theory for the interlaminar stresses through the thickness and across the interfaces of antisymmetric angle-ply laminates with free edges.

Boundary scattering in the SU(N) Principal Chiral Model on the half-line with conjugating boundary conditions

We investigate the SU(N) Principal Chiral Model on a half-line with a particular set of boundary conditions (BCs). In previous work these BCs have been shown to correspond to boundary scattering matrices (K-matrices) which are representation conjugating and whose matrix structure corresponds to one of the symmetric spaces SU(N)/SO(N) or SU(N)/Sp(N). Starting from the bulk particle spectrum and the K-matrix for a particle in the vector representation we construct K-matrices for particles in higher rank representations scattering off the boundary. We then perform an analysis of the physical strip pole structure and provide a complete set of boundary Coleman–Thun mechanisms for those poles which do not correspond to particles coupling to the boundary. We find that the model has no non-trivial boundary states.

Thermal Diffusion and Associated Stress Field due to High Speed Source

This paper presents a simple model of the thermal transport caused by a source moving at high speeds along an infinite half-space. The steady-state solution is obtained and examined to determine the effects of source velocity on the effective thermal penetration depth. The temperature field produced for a particular set of boundary conditions is then expanded to indicate how an abrupt temperature application can create a stress wave response incorporating the relationships included in a well-known hydrocode.

Fast-phase space computation of multiple arrivals.

We present a fast, general computational technique for computing the phase-space solution of static Hamilton-Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive "Escape Equations" which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a "one-pass" formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation.

The electro-mechanical impedance method for damage identification in circular plates

Among structural acoustics methods, the electromechanical (E/M) impedance method is a new method that is easy to implement on complex structures with minimum instrumentation and straightforward results. This new acoustic method benefits from the advent of commercially available low-cost piezoceramics that have opened new opportunities for structural identification. The structural dynamics is identified by obtaining the E/M impedance or admittance signatures of piezoelectric active sensors that are permanently attached to the structure. In the presented study, the E/M impedance method was used to identify the structural dynamics and the presence of damage in circular plates. An analytical expression, which accounts for both axial and flexural vibrations of a plate, was derived and validated through a set of experiments. The experimental results show good matching with the theory. Additional acoustic experiments were conducted to assess the presence of damage in circular plates for a particular set of boundary conditions. Some damage metrics were suggested to analyze the frequency spectrum obtained. The results show the changes in the E/M impedance spectrum due to damage presence. Future research will focus on the application of the E/M impedance to the acoustical diagnostics of aging aircraft structures.