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At least 541 records · Page 30

Sufficient conditions for a local minimum of the Bolza problem with a variable initial point

Sufficient conditions for a weak relative minimum of a form of the Bolza problem of variational calculus are derived. The variational problem considered includes arbitrary numbers of constraints on the initial and terminal points, but assumes no control constraints or interior point constraints. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of previously published sets of conditions. The derivation, though lengthy, is felt to be simpler in concept than previous derivations. The application of these conditions is demonstrated in the context of a simple geometric problem.

Wood, Lincoln J.↗

Weak scale as a trigger

Does the value of the Higgs mass parameter affect the expectation value of local operators in the Standard Model? For essentially all local operators the answer to this question is "no", and this is one of the avatars of the hierarchy problem: nothing is "triggered" when the Higgs mass parameter crosses zero. In this letter, we explore settings in which Higgs mass parameters $can$ act as a "trigger" for some local operators ${\cal O}_T$. In the Standard Model, this happens for ${\cal O}_T = {\rm Tr} (G \tilde G)$. We also introduce a "type-0" two Higgs doublet model, with a $Z_4$ symmetry, for which ${\cal O}_T = H_1 H_2$ is triggered by the Higgs masses, demanding the existence of new Higgs states necessarily comparable to or lighter than the weak scale, with no wiggle room to decouple them whatsoever. Surprisingly, this model is not yet entirely excluded by collider searches, and will be incisively probed by the high-luminosity run of the LHC, as well as future Higgs factories. We also discuss a possibility for using this trigger to explain the origin of the weak scale, invoking a landscape of extremely light, weakly interacting scalars $\phi_i$, with a coupling to ${\cal O}_T$ needed to make it possible to find vacua with small enough cosmological constant. The weak scale trigger links the tuning of the Higgs mass to that of the cosmological constant, while coherent oscillations of the $\phi_i$ can constitute dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Supply sunspots and shadows: Business siting patterns and inequitable rooftop solar adoption in the United States

Entrepreneurs in certain industries tend to locate new businesses in relatively affluent areas. Preferences to site businesses in affluent areas can reduce low-income household access to certain products. Some argue that business siting patterns could explain inequitable consumption patterns, though such causal claims are often empirically weak. Here, we explore whether business siting patterns partly explain inequitable adoption of rooftop solar photovoltaics in California. We show that solar business formation drives an immediate and sustained increase in local solar adoption, including in low-income areas. However, solar business siting patterns have only weak impacts on solar adoption equity. The data show how solar businesses headquartered in low-income areas nonetheless install solar for relatively affluent customers. Customer-level adoption inequity partly offsets the potential equity gains of siting more businesses in low-income areas. We discuss how the emergent nature and unique business model of rooftop solar help explain these nuanced results.

14 SOLAR ENERGY↗

TYPE III RADIO BURSTS PERTURBED BY WEAK CORONAL SHOCKS

Some type III bursts are observed to undergo sudden flux modifications, e.g., reductions and intensifications, when type III beams cross shocks in the upper corona or solar wind. First simulations are presented for type III bursts perturbed by weak coronal shocks, which type III beams traverse. The simulations incorporate spatially localized jumps in plasma density and electron and ion temperatures downstream of a shock. A shock is predicted to produce significant modulations to a type III burst: (1) a broadband flux reduction or frequency gap caused by the shock's density jump, (2) a narrowband flux intensification originating from where the downstream plasma density locally has a small gradient, (3) a possible intensification from the shock front or just upstream, and (4) changes in the frequency drift rate profile and the temporal evolution of radiation flux at frequencies corresponding to the shocked plasma. The modulations are caused primarily by fundamental modifications to the radiation processes in response to the shocked density and temperatures. The predicted intensifications and reductions appear qualitatively consistent with the available small number of reported observations, although it is unclear how representative these observations are. It is demonstrated that a weak shock can cause an otherwise radio-quiet type III beam to produce observable levels of narrowband radio emission. The simulations suggest that type III bursts with frequency-time fine structures may provide a tool to probe shocks in the corona and solar wind, especially for weak shocks that do not radiate by themselves.

79 ASTRONOMY AND ASTROPHYSICS↗

Structural transition, subgap states, and carrier transport in anion-engineered zinc oxynitride nanocrystalline films

In this work, anion alloying is engineered in ZnON nanocrystalline films, and the resultant evolution of the structural transition, subgap states, and carrier transport is investigated. A broad distribution of sub-gap states above the valence band maximum is introduced by nitrogen due to the hybridization of N 2p and O 2p orbitals. The phase transition from partially amorphous states to full crystallinity occurs above a characteristic growth temperature of 100 °C, and the localized states are suppressed greatly due to the reduction of nitrogen composition. The electronic properties are dominated by grain boundary scattering and electron transport across boundary barriers through thermal activation at band edge states at high temperatures. The conductivity below 130 K exhibits a weak temperature dependence, which is a signature of variable-range hopping conduction between localized states introduced by nitrogen incorporation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Forward-Backward Asymmetry at High Mass in $t\bar{t}$ Production in $p\bar{p}$ Collisions at $\sqrt{s} = 1.96$ TeV

Current understanding of particle physics postulates that there are 17 fundamental particles that interact via four fundamental forces - gravity, the strong force, the weak force, and the electromagnetic force. These fundamental particles can be classified by their spins into bosons, which are the force-carrying particles with integer spins, and fermions, which have half-integer spins. Fermions can be further divided into quarks and leptons. The particles and three of the four forces - all but gravity - are described by the Standard Model, a local SU(3) x SU(2) x U(1) gauge theory. Electromagnetic and weak interactions as described by Electroweak Theory or Quantum Electrodynamics, SU(2) x U(1). Strong interactions are described by Quantum Chromodynamics or QCD, SU(3). Fermions are grouped into three generations as shown in Table 1.1. Each generation consists of a leptonic doublet containing a charged and a neutral lepton and a weak isospin doublet containing two quarks. The first generation, containing the electron, the electron neutrino, the up quark, and the down quark, is the lightest generation and is thus the most frequently found in nature. The second generation contains the muon, the muon neutrino, the strange quark, and the charm quark. The third generation contains the tau, the tau neutrino, the bottom quark, and the top quark.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Rate-dependent strength and deformation heterogeneity of B4C-reinforced Al composite: Time-resolved imaging with synchrotron X-rays

Dynamic (up to 5500 s -1 ) and quasi-static compression tests are conducted on a 15 wt% B4C particle-reinforced Al (B 4 C/Al) composite. In situ, high-speed synchrotron X-ray phase contrast imaging and digital image correlation are employed to map mesoscale deformation fields at μm and μs scales. The bulk stress–strain curves show significant strain and strain-rate hardening under dynamic compression. The strain-rate sensitivity exponent is an order of magnitude higher at high strain rates (> 10 3 s -1 ) than that at low strain rates (< 10 -2 s -1 ). Strain field mapping demonstrates distinct compressive strain localizations for both quasi-static and dynamic loading. Nevertheless, compressive strain localizations appear denser in spacing under dynamic loading, owing to spontaneous dislocation nucleation in both weak and strong zones. This results in a higher density of geometrically necessary dislocations, which contributes to the higher strain and strain-rate hardening of B 4 C/Al under dynamic loading. Additionally, the ratio of the maximum local strain to the bulk average is 1.5, and the local strain-rate enhancement cannot explain the increased rate sensitivity of B 4 C/Al under dynamic loading. Therefore, the rate-dependent deformation heterogeneity dominates the strain-rate hardening of B 4 C/Al. Postmortem analyses help correlate deformation features to particle- and grain-scale microstructures, yielding consistent results with mesoscale strain fields.

36 MATERIALS SCIENCE↗

Influence of local lattice distortions on electrical transport of refractory high entropy alloys

In this report we employ first-principles alloy theories to assess the influence of local lattice distortions on the electronic transport of six body-centered cubic high-entropy alloys. We find weak disorder smearing of bands in the ideal lattice due to the similar number of valence electrons among alloying elements. Allowing relaxation, we demonstrate that local distortions in NbMoTaW and VNbMoTaW are small while they are anomalously large in HfNbTiZr, HfNbTaTiZr, VCrZrNb and CrNbTiVZr. The Fermi surfaces of the latter are strongly smeared by local distortions, leading to nearly-saturated resistivities. These findings address the important local relaxation effect on the electronic structure of high-entropy alloys.

36 MATERIALS SCIENCE↗

Detection and Signal Processing for Near-Field Nanoscale Fourier Transform Infrared Spectroscopy

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering-type near-field infrared spectroscopic techniques to characterize materials non-destructively with nanoscale spatial resolution. However, a sub-optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR) are outlined. The self-contained mathematical and experimental work derives and explains: i) how normalized complex-valued nano-FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano-FTIR. The algebraic model for weak oscillators is validated with nano-FTIR and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.

36 MATERIALS SCIENCE↗

Tip‐Enhanced Imaging and Control of Infrared Strong Light‐Matter Interaction

Optical antenna resonators enable control of light‐matter interactions on the nano‐scale via electron–photon hybrid states in strong coupling. Specifically, mid‐infrared (MIR) nano‐antennas coupled to saturable intersubband transitions in multi‐quantum‐well (MQW) semiconductor heterostructures allow for the coupling strength to be tuned through antenna resonance and field intensity. Here, in this study, tip‐enhanced nano‐scale variation of antenna‐MQW coupling across the antenna is demonstrated, with a spatially‐dependent coupling strength $g_{\textrm{aq}}$ varying from 73 (strong coupling) to 24 cm -1 (weak coupling). This behavior is modeled based on the spatially dependent local constructive and destructive interference between tip and antenna fields. Using a quantum‐mechanical density‐matrix model of the MQW system with its designed values of transition dipole moment, doping density, and population decay time, the picosecond IR pulse coupling to intersubband transitions and the associated tip induced strong‐field saturation effects are described. These results present a new regime of nonlinear IR light‐matter control based on the dynamic manipulation of quantum hybrid states on the nanoscale and in the infrared, with a perspective regarding extension to molecular vibrations.

Wang, Yueying↗

Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

97 MATHEMATICS AND COMPUTING↗

How Well Does Kohn–Sham Regularizer Work for Weakly Correlated Systems?

Kohn–Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn–Sham density functional theory that works for strongly correlated systems. Here we test KSR for a weak correlation. We propose spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations found by minimizing density and total energy loss. We assess the atoms-to-molecules generalizability by training on one-dimensional (1D) H, He, Li, Be, and Be 2+ and testing on 1D hydrogen chains, LiH, BeH 2 , and helium hydride complexes. The generalization error from our semilocal approximation is comparable to other differentiable approaches, but our nonlocal functional outperforms any existing machine learning functionals, predicting ground-state energies of test systems with a mean absolute error of 2.7 mH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fault Stability Perturbation by Thermal Pressurization and Stress Transfer Around a Deep Geological Repository in a Clay Formation

The increase of temperature of a low-permeability, fluid-saturated media may trigger significant thermal pressurization, where the expansion of pore fluid cannot be accommodated by the thermal expansion of the pore space. With the aid of a coupled thermohydromechanical numerical simulator, we investigate the possible impact of thermal pressurization during the life of a deep geological repository (DGR) for high-level radioactive waste, characterized by the emplacement of radioactive material-filled canisters in a series of parallel tunnels, excavated in a low-permeability clay formation. We represent the fault as a planar structure embedded in a thermoporoelastic material and shear activation evaluated by a strain-softening Mohr-Coulomb failure criterion. The results show that stress changes caused by temperature and thermal pressurization of a rock mass around the emplacement tunnels may trigger a slip event on a fault plane in proximity of the geological disposal site: Rupture nucleates at depth, hundreds of meters below the DGR. Stress transfer plays a key role, while a direct hydraulic connection between the repository and the nucleation zone is not necessary in order to trigger rupture. A low stress ratio may favor the occurrence of slip up to a distance of 600 m of the fault from the outermost tunnel. Furthermore, these results highlight the need of investigating hydromechanical properties and local stress conditions at depth to characterize the geomechanical response of weak planes located in the surroundings of a high-level radioactive waste repository and to provide sufficient knowledge for the safe development of the DGR site.

58 GEOSCIENCES↗

High-energy electron emission from metallic nano-tips driven by intense single-cycle terahertz pulses

Electrons ejected from atoms and subsequently driven to high energies in strong laser fields enable techniques from attosecond pulse generation to imaging with rescattered electrons. Analogous processes govern strong-field electron emission from nanostructures, where long wavelength radiation and large local field enhancements hold the promise for producing electrons with substantially higher energies, allowing for higher resolution time-resolved imaging. Here we report on the use of single-cycle terahertz pulses to drive electron emission from unbiased nano-tips. Energies exceeding 5 keV are observed, substantially greater than previously attained at higher drive frequencies. Despite large differences in the magnitude of the respective local fields, we find that the maximum electron energies are only weakly dependent on the tip radius, for 10 nm<R<1,000 nm. As a result, due to the single-cycle nature of the field, the high-energy electron emission is predicted to be confined to a single burst, potentially enabling a variety of applications.

36 MATERIALS SCIENCE↗

Noncommutative Common Cause Principles in algebraic quantum field theory

States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Characterization of radial turbulent fluxes in the Santander linear plasma machine

It is shown that the statistical and correlation properties of the local turbulent flux measured at different radial locations of the cold, weakly ionized plasmas inside the Santander Linear Plasma Machine [Castellanos et al., Plasma Phys. Control. Fusion 47, 2067 (2005)] are consistent with diffusive-like transport dynamics. This is in contrast to the dynamical behavior inferred from similar measurements taken in hotter, fully ionized tokamak and stellarator edge plasmas, in which long-term correlations and other features characteristic of complex, non-diffusive transport dynamics have been reported in the past. These results may shed some light on a recent controversy regarding the possible universality of the dynamics of turbulent transport in magnetized plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaric-isothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗