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A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.
The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
The state-of-the-art in stratospheric balloon-borne vector electric field measurements, from its origins to the present is reviewed. Consideration is given to the Extended Life Balloon-Borne Observatories program that utilizes an extensively modified payload and dual telemetry systems to improve the measurements and increase the data rates.
The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will map sources in multiband colour--variability space. We present a prototype coherence-based framework for astrobiology and technosignature searches, in which candidates are treated as structured departures from natural astrophysical manifolds rather than isolated photometric outliers. We illustrate the framework with three simulated cases: five Kuiper Belt Object (KBO) surface/activity states, a grid of 649 synthetic exoplanet spectra with vegetation-red-edge-like (VRE) perturbations, and 500 synthetic multiband light curves, each projected into LSST-like observable space and analysed through colour geometry, chromatic variability, and cross-band coherence. Key results include a full-colour Mahalanobis distance $D\approx5.1$ for the weak-coma KBO state (${\sim}5σ$ in the five-dimensional colour vector), an indicative VRE coherence threshold at $f_{\rm crit}\approx0.13$, and an idealised stacking forecast reaching $5σ$ under optimistic assumptions. We show, using a small Gaia~DR3 stellar sample, that stellar colour and photometric stability may inform the prioritisation of Galactic regions for applying such coherence diagnostics.
The majority of state-of-the-art speaker recognition systems (SR) utilize speaker models that are derived from an adapted universal background model (UBM) in the form of a Gaussian mixture model (GMM). This is true for GMM supervector systems, joint factor analysis systems, and most recently i-vector systems. In all of the identified systems, the posterior probabilities and sufficient statistics calculations represent a computational bottleneck in both enrollment and testing. We propose a multi-layered hash system, employing a tree-structured GMM–UBM which uses Runnalls’ Gaussian mixture reduction technique, in order to reduce the number of these calculations. Moreover, with this tree-structured hash, we can trade-off reduction in computation with a corresponding degradation of equal error rate (EER). As an example, we also reduce this computation by a factor of 15× while incurring less than 10% relative degradation of EER (or 0.3% absolute EER) when evaluated with NIST 2010 speaker recognition evaluation (SRE) telephone data.
Inclusive production processes will be important for the first observations of X Y Z states at new generation electron-hadron colliders, as they generally benefit from larger cross sections than their exclusive counterparts. We make predictions of semi-inclusive photoproduction of the χ c 1 ( 1 P ) and X ( 3872 ) , whose peripheral production is assumed to be dominated by vector exchanges. We validate the applicability of vector meson dominance in the axial-vector charmonium sector and calculate production rates at center-of-mass energies relevant for future experimental facilities. We find the semi-inclusive cross sections near the threshold to be enhanced by a factor of ∼ 2 – 3 compared to the exclusive reaction and well-suited for a first observation in photoproduction. Published by the American Physical Society 2024
A two-dimensional electron gas (2DEG) with equal-strength Rashba and Dresselhaus spin-orbit coupling sustains persistent helical spin-wave states, which have remarkably long lifetimes. In the presence of an in-plane magnetic field, there exist single-particle excitations that have the character of propagating helical spin waves. For magnon-like collective excitations, the spin-helix texture reemerges as a robust feature, giving rise to a decoupling of spin-orbit and electronic many-body effects. We prove that the resulting spin-flip wave dispersion is the same as in a magnetized 2DEG without spin-orbit coupling, apart from a shift by the spin-helix wave vector. The precessional mode about the persistent spin-helix state is shown to have an energy given by the bare Zeeman splitting, in analogy with Larmor’s theorem. Lastly, we also discuss ways to observe the spin-helix Larmor mode experimentally.
Here we report the discovery of CeLiBi 2 , the first example of a material in the tetragonal CeTX 2 ( T = transition metal; X = pnictogen) family wherein an alkali cation replaces the typical transition metal. Magnetic susceptibility and neutron powder diffraction measurements are consistent with a crystal-field Γ 6 ground-state Kramers doublet that orders antiferromagnetically below T N = 3.4 K with an incommensurate propagation wave vector k = ( 0, 0.0724(4), 0.5) that generates a nanometric modulation of the magnetic structure. The best model of the ordered state is an elliptical cycloid with Ce moments primarily residing in the ab plane. This is highly unusual, as all other Γ 6 CeTX 2 members order ferromagnetically. Further, we observe an atypical hard-axis metamagnetic transition at 2 T in magnetostriction, magnetization, and resistivity measurements. CeLiBi 2 is a rare example of a highly conductive material with dominant skew scattering leading to a large anomalous Hall effect. Quantum oscillations with five frequencies arise in magnetostriction and magnetic susceptibility data to T = 30 K and μ 0 H = 55 T, which indicate small Fermi pockets of light carriers with effective masses as low as 0.07 m e . Density functional theory calculations indicate that square-net Dirac-like Bi-p bands are responsible for these ultralight carriers. Together, our results show that CeLiBi 2 enables multiple atypical magnetic and electronic properties in a single clean material.
We discuss thermofield double QFT at real time, in the large N limit. First, we establish a (dynamical) symmetry, which we argue holds in general for the real-time portion of the Schwinger–Kelydish contour. At large N, this symmetry is seen to generate a one-parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on an example of the O(N) vector QFT. As a nontrivial application, we describe the construction of the corresponding (large N) thermofield double state in real-time collective formalism.
The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.
Herein we investigate coupled electron-lattice dynamics in the topological insulator Bi 2 Te 3 with time-resolved photoemission and time-resolved x-ray diffraction. It is well established that coherent phonons can be launched by optical excitation, but selection rules generally restrict these modes to zone-center wave vectors and Raman-active branches. We find that the topological surface state couples to additional modes, including a continuum of surface-projected bulk modes from both Raman and infrared branches, with possible contributions from surface-localized modes when they exist. Our calculations show that this surface vibrational spectrum occurs naturally as a consequence of the translational and inversion symmetries broken at the surface, without requiring the splitting-off of surface-localized phonon modes. The generality of this result suggests that coherent phonon spectra are useful by providing unique fingerprints for identifying surface states in more controversial materials. These effects may also expand the phase space for tailoring surface state wave functions via ultrafast optical excitation.
It is established that the problem of elastic oscillations of a homogeneous anisotropic semicylinder (console) with traction-free lateral surface (Neumann boundary condition) has no eigenvalues when the console is clamped at one end (Dirichlet boundary condition). If the end is free, under additional requirements of elastic and geometric symmetry, simple sufficient conditions are found for the existence of an eigenvalue embedded in the continuous spectrum and generating a trapped elastic wave, that is, one which decays at infinity at an exponential rate. The results are obtained by generalizing the methods developed for scalar problems, which however require substantial modification for the vector problem in elasticity theory. Examples are given and open questions are stated. Bibliography: 53 titles.
Neutron scattering studies were carried out for investigating heavy-electron-like behaviors of PrCu4Au. Excitation spectra are composed of crystal-field (CF) excitations in the Pr3+4f2 electron configuration and a broad component. The CF splitting ground state is a triplet 5. The type-II antiferromagnetic ordering characterized by the propagation vector (1/2, 1/2, 1/2) appears below approximately 4 K. The powder diffraction pattern is reproduced by the ordered magnetic moments aligning along the direction perpendicular to the propagation vector. The magnitude of the ordered magnetic moment is evaluated as 1.36uB/Pr, which is less than 2.0uB/Pr expected from the 5 ground state. Dual electronic states of both localized and itinerant character are inferred.
To supplement previous work performed by NASA, a cold-jet facility was established at the California Polytechnic State University, San Luis Obispo campus. The purpose of this facility is to continue the studies of cold flow multiaxis thrust vectoring conducted at the NASA Langley Research Center. A single nozzle test apparatus was completed and is presently operational. Included are the results of the single flow test envelope that was requested by NASA personnel. Details about the test apparatus are included in the Cal Poly Semi-Annual Progress report.
Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of 3He-A, the coherent quantum state no longer supports persistent superflow. In this paper, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. Specifically, we introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. Here, we apply this idea to the case of SmB6, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.
A reaction microscope (ReMi) has been combined with a magneto-optical trap (MOT) for the kinematically complete investigation of atomic break-up processes. With the novel MOTReMi apparatus, the momentum vectors of the fragments of laser-cooled and state-prepared lithium atoms are measured in coincidence and over the full solid angle. The first successful implementation of a MOTReMi could be realized due to an optimized design of the present setup, a nonstandard operation of the MOT, and by employing a switching cycle with alternating measuring and trapping periods. The very low target temperature in the MOT (∼2 mK) allows for an excellent momentum resolution. Optical preparation of the target atoms in the excited Li 2{sup 2}P{sub 3/2} state was demonstrated providing an atomic polarization of close to 100%. While first experimental results were reported earlier, in this work, we focus on the technical description of the setup and its performance in commissioning experiments involving target ionization in 266 nm laser pulses and in collisions with projectile ions.
In this article, we have investigated the magnetic ground state of the antiferromagnetic Kondo-lattice compounds CeMAl 4 Si 2 (M = Rh, Ir) using neutron powder diffraction. Although both of these compounds show two magnetic transitions T N1 and T N2 in the bulk properties measurements, evidence for magnetic long-range order was only found below the lower transition T N2 . Analysis of the diffraction profiles reveals a commensurate antiferromagnetic structure with a propagation vector k = (0, 0, 1/2). The magnetic moment in the ordered state of CeRhAl 4 Si 2 and CeIrAl 4 Si 2 were determined to be 1.14(2) and 1.41(3) μB /Ce, respectively, and are parallel to the crystallographic c-axis in agreement with magnetic susceptibility measurements.
This article presents the results of transient dynamic simulations of loads due to disruption eddy currents on the NSTXU vacuum vessel. Dynamic loading at diagnostic mounting locations is expressed as response spectra derived from the time history results of the dynamic structural simulations of a variety of disruption scenarios. The disruption simulations draw on a history of the project assessments of worst case disruptions for specific components. Major efforts to assess disruption loading have included the vacuum vessel which is the major structural support for the machine, as well as the passive plates (PPs), high harmonic fast wave (HHFW) antenna, and centerstack casing. Each one of these efforts included transient electromagnetic simulations producing time-dependent eddy current Lorentz loads (and in some cases halo loads) which then were applied to time-dependent structural dynamic analyses intended to obtain the proper dynamic amplification factors. In some instances, the EM model and structural model were identical allowing direct transfer of EM forces to the structural model. In other cases, the EM and structural model were not identical and the vector potential (VP) transfer method was used. The results files from these analyses were available (or re-run) to post process in ANSYS Classic time history postprocessor. In conclusion, the ANSYS command is used to create response spectra from time history data at desired points on the vessel.