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Realization of the orbital-selective Mott state at the molecular level in Ba3LaRu2O9
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Realization of a wide steering end-fire facet optical phased array using silicon rich silicon nitride
The design, fabrication, and characterization of a 16-element optical phased array (OPA) using a high index (n = 3.1) silicon-rich silicon nitride (SRN) is demonstrated. Here, we present one-dimensional beam steering with end-fire facet antennas over a wide steering range of >115° at a fixed wavelength of 1525 nm. A beam width of 6.3° has been measured at boresight, consistent with theory. We demonstrate SRN as a viable material choice for chip-scale OPA applications due to its high thermo-optic coefficient, high optical power handling capacity [negligible two-photon absorption (TPA)], wide transparency window, and CMOS compatibility.
Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2(r)$ or its corresponding structure factor $\textit{S(k)}$ is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including $\textit{d}$-dimensional Gaussian structure factors, $\textit{d}$-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the $\textit{d}$-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. In this work, our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for $g_2(r)$ and $\textit{S(k)}$ associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.
New results on the realizability of Reynolds stress turbulence closures
The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.
Optimal Realization of Yang–Baxter Gate on Quantum Computers
Quantum computers provide a promising method to study the dynamics of many-body systems beyond classical simulation. On the other hand, the analytical methods developed and results obtained from the integrable systems provide deep insights on the many-body system. Quantum simulation of the integrable system not only provides a valid benchmark for quantum computers but is also the first step in studying integrable-breaking systems. The building block for the simulation of an integrable system is the Yang–Baxter gate. It is vital to know how to optimally realize the Yang–Baxter gates on quantum computers. Based on the geometric picture of the Yang–Baxter gates, the optimal realizations of two types of Yang–Baxter gates with a minimal number of controlled NOT (CNOT) or gates are presented. It is also shown how to systematically realize the Yang–Baxter gates via the pulse control. The different realizations on IBM quantum computers are tested and compared. It is found that the pulse realizations of the Yang–Baxter gates always have a higher gate fidelity compared to the optimal CNOT or realizations. On the basis of the above optimal realizations, the simulation of the Yang–Baxter equation on quantum computers is demonstrated. Finally, these results provide a guideline and standard for further experimental studies based on the Yang–Baxter gate.
Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity
Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.
A unified realization of electrical quantities from the quantum International System of Units
In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm’s law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here, in this study, we report a unified realization of the volt, ohm and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 μV V −1 . The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 μΩ Ω −1 . We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33–252 nA, and our lowest uncertainty is 4.3 μA A −1 at 83.9 nA. For other current values, a systematic error that ranges from −10 μA A −1 to −30 μA A −1 is present due to the imperfect isolation of the PJVS microwave bias.
Integrating Realizability Checking in FRET
Realizability (alternatively referred to as relative consistency or implementability) - checking whether a specification can be implemented by an open system - has been the subject of extensive study. Realizability can be viewed as a stronger analysis method when compared to consistency checking in that it does not only check whether the system works in some environment, but instead whether the system works in all environments. In this report, we experiment and build on the approach presented by Gacek et al. that supports checking realizability of contracts involving infinite theories using SMT solvers. In particular, we 1) extend the Formal Requirements Elicitation Tool (FRET) to support generation of Lustre contracts that can be checked for realizability with the JKind k-induction and fix point generation engines; 2) study a compositional way for checking realizability based on the notion of connected components; and 3) test our approach and the capabilities of the JKind realizability engines on a large subset of the Lockheed Martin Cyber Physical System Challenge Problems.
The use of the QR factorization in the partial realization problem
The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction.
Realizing the Dream of Flight: Biographical Essays in Honor of the Centennial of Flight, 1903-2003
While growing up in Cedar Rapids, Iowa, Milton Wright, The Wright Brothers Father, liked to purchase toys for his sons that he hoped would stimulate their imagination. One of the most memorable gifts was a toy helicopter that was designed by the French aeronautical experimenter Alphonse P naud. Milton gave his sons this gift in 1878, and, though it was a simple device with a stick bound to a four-blade rotor set in a spindle, it had the intended effect it caused them to dream. Twenty-five years separated the gift of this toy and their invention of the airplane, yet the Wright brothers were convinced it had exerted an important influence. Tom Crouch argued in The Bishop's Boys that toys like these perfectly illustrated the significance of play for technological innovation. He wrote, rotary-wing toys were to intrigue and inspire generations of children, a few of whom would, as adults, attempt to realize the dream of flight for themselves. If the first powered flight on 17 December 1903 represented a childhood dream realized, it was only the first step in the rapid evolution of the airplane from their flimsy kite-like contraption of wood and cloth to jet airliners and rockets in space. And, as extraordinary as the achievement of powered flight seemed in 1903, before the end of the century, space travel also would become a dream realized. Soviet astronaut Yuri Gagarin first circumnavigated Earth in April 1961, and, eight years later, American astronauts took the first steps for humankind on the Moon. It is with great pleasure that we introduce Realizing the Dream: Biographical Essays in Honor of the Centennial of Flight. These essays in celebration of the Wright brothers first flight 100 years ago grew out of presentations by a group of prominent scholars in 2003 at a conference sponsored by the NASA History Division and held at the Great Lakes Science Center in Cleveland, Ohio. The volume focuses on the careers of some of the many men and women who helped to realize the dream of flight both through the atmosphere and beyond.
From Partial to Global Assume-Guarantee Contracts: Compositional Realizability Analysis in FRET
Realizability checking refers to the formal procedure that aims to determine whether an implementation exists, always complying to a set of requirements, regardless of the stimuli provided by the system’s environment. Such a check is essential to ensure that the specification does not allow behavior that can force the system to violate safety constraints. In this paper, we present an approach that decomposes realizability checking into smaller, more tractable problems. More specifically, our approach automatically partitions specifications into sets of non-interfering requirements. We prove that checking whether a specification is realizable reduces to checking that each partition is realizable.We have integrated realizability checking and implemented our decomposition approach within the open-source Formal Requirements ElicitationTool (FRET). A FRET user may check the realizability of a specification monolithically or compositionally. We evaluate our approach by comparing monolithic and compositional checking and showcase the strengths of our decomposition approach on a variety of industrial-level case studies
Three-dimensional realizations of flood flow in large-scale rivers using the neural fuzzy-based machine-learning algorithms
Machine learning methods have been extensively used to study the dynamics of complex fluid flows. One such algorithm, known as adaptive neural fuzzy inference system (ANFIS), can generate data-driven predictions for flow fields, but has not been applied to natural geophysical flows in large-scale rivers. Herein, we demonstrate the potential of ANFIS to produce three-dimensional (3D) realizations of the instantaneous flood flow field in several large-scale, virtual meandering rivers. The 3D dynamics of flood flow in large-scale rivers were obtained using large-eddy simulation (LES). The LES results, i.e., the 3D velocity components, were employed to train the learnable coefficients of an ANFIS. Further, the trained ANFIS, along with a few time-steps of LES results (precursor data) were then used to produce 3D realizations of flood flow fields in large-scale rivers with geometries other than the one the ANFIS was trained with. We also used the trained ANFIS to generate 3D realizations of river flow at a discharge other than that the ANFIS was trained with. The flow field results obtained from ANFIS were validated using separate LES runs to assess the accuracy of the 3D instantaneous realizations of the machine learning algorithm. An error analysis was conducted to quantify the discrepancies among the ANFIS and LES results for various flood flow predictions in large-scale rivers.
Eigensystem realization algorithm user's guide forVAX/VMS computers: Version 931216
The eigensystem realization algorithm (ERA) is a multiple-input, multiple-output, time domain technique for structural modal identification and minimum-order system realization. Modal identification is the process of calculating structural eigenvalues and eigenvectors (natural vibration frequencies, damping, mode shapes, and modal masses) from experimental data. System realization is the process of constructing state-space dynamic models for modern control design. This user's guide documents VAX/VMS-based FORTRAN software developed by the author since 1984 in conjunction with many applications. It consists of a main ERA program and 66 pre- and post-processors. The software provides complete modal identification capabilities and most system realization capabilities.
The Wettzell System Monitoring Concept and First Realizations
Automated monitoring of operational system parameters for the geodetic space techniques is becoming more important in order to improve the geodetic data and to ensure the safety and stability of automatic and remote-controlled observations. Therefore, the Wettzell group has developed the system monitoring software, SysMon, which is based on a reliable, remotely-controllable hardware/software realization. A multi-layered data logging system based on a fanless, robust industrial PC with an internal database system is used to collect data from several external, serial, bus, or PCI-based sensors. The internal communication is realized with Remote Procedure Calls (RPC) and uses generative programming with the interface software generator idl2rpc.pl developed at Wettzell. Each data monitoring stream can be configured individually via configuration files to define the logging rates or analog-digital-conversion parameters. First realizations are currently installed at the new laser ranging system at Wettzell to address safety issues and at the VLBI station O Higgins as a meteorological data logger. The system monitoring concept should be realized for the Wettzell radio telescope in the near future.
Better bang for your buck? Comparing savings realization from ESPCs and direct-funded projects
Energy savings performance contracts (ESPCs) offer an opportunity to tremendously scale decarbonization projects, given their paid-from-savings premise. However, prospective customers still question whether ESPC is worth the effort and expense. This study evaluates the savings realization rates of ESPCs compared to direct-funded projects using ENERGY STAR Portfolio Manager (ESPM) benchmarking data. It compares normalized EUIs from ESPM before and after energy conservation projects implemented via ESPC or direct funding in roughly 450 federal buildings. This documented change, ideally a savings, can then be compared to the estimated savings from the energy conservation initiative in order to generate a rough realization rate. Preliminary results indicate a notably greater savings realization rate for the ESPC buildings (median = 105% of estimated savings) than those that underwent direct-funded projects (median = 46%). Because of a shortage of good quality data and the wide range in results, the difference is only significant at the p < 0.20 level. However, the higher savings realization of ESPCs corroborates the authors’ 2014 findings using a different comparison method. With continued soft government funding and regulatory impediments for climate change mitigation in the U.S., financed, paid-from-savings project models (e.g., ESPC, PACE, EaaS and others) certainly merit more attention. This study’s results are particularly compelling (and encouraging) given the country’s likely reliance on these vehicles to address existing building retrofits.
Compositional Realizability Checking within FRET
A set of requirements for a reactive system is realizable if, for any sequence of inputs that satisfy the assumptions on the environment, the guarantees always hold. Realizability checking is essential to ensure that an implementation can be constructed that satisfies the requirements. We propose a framework that supports users in the non-trivial task of developing realizable requirements. Our framework uses architectural information to automatically de-compose a set of requirements into subsets that can be analyzed separately, and therefore more efficiently. It then integrates existing algorithms in order to detect unrealizability, identify minimal sets of conflicting requirements, and compute counterexamples. The capability to focus on minimal conflict sets is key for localizing and correcting the sources of unrealizability. Our approach supports this process by enabling users to interactively visualize and explore the produced conflict sets and counterexamples. We have implemented our framework in the open-source Formal Requirements Elicitation Tool (FRET), and have used it on a variety of industrial-level case studies, showcasing the strengths of our approach in terms of raw performance, as well as diagnostic potential.
Realizability Checking of Requirements in FRET
Requirements formalization has become increasingly popular in industrial settings as an effort to disambiguate designs and optimize development time and costs for critical system components. Formal requirements elicitation also enables the employment of analysis tools to prove important properties, such as consistency and realizability. In this report, we present the realizability analysis framework that we developed as part of the Formal Requirements Elicitation Tool (FRET). Our framework prioritizes usability, and employs state-of-the-art analysis algorithms that support infinite theories. We demonstrate the workflow for realizability checking, showcase the diagnosis process that supports visualization of conflicts between requirements and simulation of counterexamples, and discuss results from industrial-level case studies.