On estimating the region of asymptotic stability using Liapunov's method.
Region of asymptotic stability estimation as minimization problem, using Liapunov method
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Region of asymptotic stability estimation as minimization problem, using Liapunov method
Neuroendocrine tumors (NETs) express somatostatin receptors (SSTRs) 2 and 5. Modified variants of somatostatin, the cognate ligand for SSTR2 and SSTR5, are used in treatment for metastatic and locoregional disease. Peptide receptor radionuclide therapy with 177 Lu-DOTATATE (DOTA-octreotate), a β-particle–emitting somatostatin derivative, has demonstrated survival benefit in patients with SSTR-positive NETs. Despite excellent results, a subset of patients has tumors that are resistant to treatment, and alternative agents are needed. Targeted α-particle therapy has been shown to kill tumors that are resistant to targeted β-particle therapy, suggesting that targeted α-particle therapy may offer a promising treatment option for patients with 177 Lu-DOTATATE–resistant disease. Although DOTATATE can chelate the clinically relevant α-particle–emitting radionuclide 225 Ac, the labeling reaction requires high temperatures, and the resulting radioconjugate has suboptimal stability. Methods: We designed and synthesized MACROPATATE (MACROPA-octreotate), a novel radioconjugate capable of chelating 225 Ac at room temperature, and assessed its in vitro and in vivo performance. Results: MACROPATATE demonstrated comparable affinity to DOTATATE (dissociation constant, 21 nM) in U2-OS-SSTR2, a SSTR2-positive transfected cell line. 225 Ac-MACROPATATE demonstrated superior serum stability at 37°C over time compared with 225 Ac-DOTATATE. Biodistribution studies demonstrated higher tumor uptake of 225 Ac-MACROPATATE than of 225 Ac-DOTATATE in mice engrafted with subcutaneous H69 NETs. Therapy studies showed that 225 Ac-MACROPATATE exhibits significant antitumor and survival benefit compared with saline control in mice engrafted with SSTR-positive tumors. However, the increased accumulation of 225 Ac-MACROPATATE in liver and kidneys and subsequent toxicity to these organs decreased its therapeutic index compared with 225 Ac-DOTATATE. Conclusion: 225 Ac-MACROPATATE and 225 Ac-DOTATATE exhibit favorable therapeutic efficacy in animal models. Because of elevated liver and kidney accumulation and lower administered activity for dose-limiting toxicity of 225 Ac-MACROPATATE, 225 Ac-DOTATATE was deemed the superior agent for targeted α-particle peptide receptor radionuclide therapy.
The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.
Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.
Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.
In its present state, the Amplification Factor Transport (AFT) model provides an efficient alternative for high-fidelity stability methods for complex geometries subject to low-speed conditions considered in the industrial-production CFD environment. Its performance has not yet been documented for the typical transition scenarios in hypersonic conditions. The goal of the present study is to apply the AFT model to a yawed- and flared-cone configuration, for which the laminar flows respectively support the crossflow and second-mode instability mechanisms, and to compare the amplification results against high-fidelity results computed with Linear Parabolized Stability Equations (LPSE). High-resolution viscous-flow solutions are provided with OVERFLOW and COFFE. For the yawed-cone case, the AFT model yields the largest amplification in a region of the flow where the expected crossflow instability is not amplified (in the leeward symmetry plane) according to LPSE. For the flared-cone case with a wall-temperature slightly lower than the adiabatic value, the AFT model yields extremely large amplification factors (in excess of 100), exceeding the computed LPSE amplification of second-mode instability results by a factor 14. Upon considering a cold-wall condition, the model shows much smaller amplification factors, which is the opposite with respect to the expected behavior of the second mode. The AFT model does not adequately capture the crossflow and second-mode instability mechanisms in its present state.
A development of the finite element method for thin shell instability analysis is presented, covering three principal aspects: (1) representation of shell geometry, (2) representation of element behavior, and (3) algorithmic tools for solution of the large-order systems of nonlinear algebraic equations which characterize various phases of shell instability. Two shell elements are described, an arbitrary quadrilateral and a triangle, and numerical results are presented for two widely-employed comparison problems for linear (stable) analysis. Two shell problems which include instability effects are also solved.-
Size-dependent phagocytosis is a well-characterized phenomenon in monocytes and macrophages. However, this size effect for preferential gene delivery to these important cell targets has not been fully exploited because commonly adopted stabilization methods for electrostatically complexed nucleic acid nanoparticles, such as PEGylation and charge repulsion, typically arrest the vehicle size below 200 nm. Here, we bridge the technical gap in scalable synthesis of larger submicron gene delivery vehicles by electrostatic self-assembly of charged nanoparticles, facilitated by a polymer structurally designed to modulate internanoparticle Coulombic and van der Waals forces. Specifically, our strategy permits controlled assembly of small poly(β-amino ester)/messenger ribonucleic acid (mRNA) nanoparticles into particles with a size that is kinetically tunable between 200 and 1,000 nm with high colloidal stability in physiological media. We found that assembled particles with an average size of 400 nm safely and most efficiently transfect monocytes following intravenous administration and mediate their differentiation into macrophages in the periphery. When a CpG adjuvant is co-loaded into the particles with an antigen mRNA, the monocytes differentiate into inflammatory dendritic cells and prime adaptive anticancer immunity in the tumor-draining lymph node. This platform technology offers a unique ligand-independent, particle-size-mediated strategy for preferential mRNA delivery and enables therapeutic paradigmsviamonocyte programming.
The problem of electrostatic wave generation by a return current driven by a small area electron beam during solar hard X-ray bursts is discussed. The marginal stability method is used to solve numerically the electron and ion heating equations for a prescribed beam current evolution. When ion-acoustic waves are considered, the method appears satisfactory and, following an initial phase of Coulomb resistivity in which T sub e/T sub i rise, predicts a rapid heating of substantial plasma volumes by anomalous ohmic dissipation. This hot plasma emits so much thermal bremsstrahlung that, contrary to previous expectations, the unstable beam-plasma system actually emits more hard X-rays than does the beam in the purely collisional thick target regime relevant to larger injection areas. Inclusion of ion-cyclotron waves results in ion-acoustic wave onset at lower T sub e/T sub i and a marginal stability treatment yields unphysical results.
Ni-rich LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811) cathodes are investigated to realize high energy density Li ion batteries for long life electric vehicle applications. However, capacity decay and thermal instability due to cathode-electrolyte interfacial degradation remain challenges that require sophisticated surface stabilization methods to address. Here, we propose a strategy, for the first time, to form an artificial Li + -conducting cathode-electrolyte interphase (ALCEI) on the NCM811 cathode surface using a nucleophilic reaction between polysulfides and vinylene carbonate (VC). Furthemore, the as-formed ALCEI layer simultaneously protects the NCM particles from electrolyte corrosion and facilitates Li + ion transport, thus enabling stable and high rate cycling of NCM811. As a result, the ALCEI-modified NCM811 cathode exhibits a high capacity (211.6 mA h g -1 at 0.1C), notable rate capability (134 mA h g -1 at 10C), and superior cycle stability (94.2% over 200 cycles at 1C). These results underscore the use of interfacial engineering in high voltage cathode material development and provide a feasible strategy for stabilizing Ni-rich cathode interfaces in practical Li ion battery applications.
Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.
Turbulence, low-temperature chemistry, and their interactions in the form of turbulent cool flames are critical to understanding and improving advanced engines. Design of such engines requires tractable simulations which in turn necessitate turbulent combustion models that can account for cool flames. While manifold-based turbulent combustion models are an attractive option for hot flames, their applicability to cool flames is not yet fully understood. This is partially due to the lack of turbulent cool flame experiments, which has made model validation difficult. This work addresses these points with a combined experimental and computational investigation of turbulent nonpremixed dimethyl ether cool flames. First, a Co-flow Axisymmetric Reactor-Assisted Turbulent (CARAT) burner is developed and tested. Turbulent cool flames are studied using the formaldehyde planar laser-induced fluorescence (PLIF), acetone PLIF, and planar Rayleigh scattering techniques. The acetone PLIF signals are converted into mixture fraction values, and measurements of time-averaged temperature are derived from the Rayleigh scattering signals by taking advantage of the similarities between cool flames and unburned mixtures. Second, a Direct Numerical Simulation (DNS) of the CARAT burner is conducted. The flame is shown to be sensitive to thermal boundary conditions such that the stabilization method is dependent on a 10 K change in inlet temperature. Comparisons of first- and second-order statistics of temperature, mixture fraction, and formaldehyde between the DNS and experiment show good agreement. The validity of manifold-based turbulent combustion models in turbulent cool flames is then explored by first studying the effective Lewis numbers in the flame using a local differential diffusion parameter analysis. Turbulent cool flames are shown to have effective unity Lewis number transport even at a much lower Reynolds number than typically required for hot flames. Good agreement is shown for temperature and formaldehyde between DNS conditional means and one-dimensional nonpremixed flame solutions. Additionally, the motion of the cool flame in mixture fraction space is shown to be well described by one-dimensional nonpremixed flame solutions. These points indicate that the fundamental physics of turbulent cool flames are analogous to turbulent hot flames, implying that the same reduced-order manifold-based modeling approaches utilized for turbulent hot flames can be utilized for turbulent cool flames.
Shape resonances in cold collisions are often strongly affected by stereodynamics. These resonances can sometimes be assigned by single-channel quantization along the scattering coordinate. However, sensitive steric control of collision implies strong anisotropy of the interaction potential energy surface, which usually leads to coupling among multiple scattering channels in the strongly interacting region. Hence, the resonances might be the result of quantization in a multidimensional space. Using the cold rotationally inelastic collision between para-H 2 (v 1 = 1, j 1 = 2) and HF (v 2 = 0, j 2 = 0) as an example, we analyze four low-lying shape resonances via diagonalization of the full-dimensional Hamiltonian with a stabilization method. While some resonances can indeed be assigned with a single partial wave, others apparently involve more than one scattering channel. Furthermore, a new model based on these resonance wavefunctions is developed to better understand the stereodynamics through shape resonances in cold collisions.
Using bacteria to transform reactive corrosion products into stable compounds represents an alternative to traditional methodsployed in iron conservation. Two environmental Aeromonas strains (CA23 and CU5) were used to transform ferric iron corrosion products (goethite and lepidocrocite) into stable ferrous iron-bearing minerals (vivianite and siderite). A genomic and transcriptomic approach was used to analyze the metabolic traits of these strains and to evaluate their pathogenic potential. Although genes involved in solid-phase iron reduction were identified, key genes present in other environmental iron-reducing species are missing from the genome of CU5. Several pathogenicity factors were identified in the genomes of both strains, but none of these was expressed under iron reduction conditions. Additional in vivo tests showed hemolytic and cytotoxic activities for strain CA23 but not for strain CU5. Both strains were easily inactivated using ethanol and heat. Nonetheless, given a lesser potential for a pathogenic lifestyle, CU5 is the most promising candidate for the development of a bio-based iron conservation method stabilizing iron corrosion. Based on all the results, a prototype treatment was established using archaeological items. On those, the conversion of reactive corrosion products and the formation of a homogenous layer of biogenic iron minerals were achieved. This study shows how naturally occurring microorganisms and their metabolic capabilities can be used to develop bio-inspired solutions to the problem of metal corrosion.
We report the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan guarantees the optimality of the finite element solution in a user-controllable energy norm, and provides several features supporting adaptive schemes. The approach provides stability automatically; there is no need for carefully derived numerical fluxes (as in DG schemes) or for mesh-dependent stabilization terms (as in stabilized methods). In this paper, we focus on features of Camellia that facilitate implementation of new DPG formulations; chief among these is a rich set of features in support of symbolic manipulation, which allow, e.g., bilinear formulations in the code to appear much as they would on paper. Many of these features are general in the sense that they can also be used in the implementation of other finite element formulations. In fact, because DPG’s requirements are essentially a superset of those of other finite element methods, Camellia provides built-in support for most common methods. We believe, however, that the combination of an essentially “hands-free” finite element methodology as found in DPG with the rapid development features of Camellia are particularly winsome, so we focus on use cases in this class. In addition to the symbolic manipulation features mentioned above, Camellia offers support for one-irregular adaptive meshes in 1D, 2D, 3D, and space-time. It provides a geometric multigrid preconditioner particularly suited for DPG problems, and supports distributed parallel execution using MPI. For its load balancing and distributed data structures, Camellia relies on packages from the Trilinos project, which simplifies interfacing with other computational science packages. Camellia also allows loading of standard mesh formats through an interface with the MOAB package. Camellia includes support for static condensation to eliminate element-interior degrees of freedom locally, usually resulting in substantial reduction of the cost of the global problem. Finally, we include a discussion of the variational formulations built into Camellia, with references to those formulations in the literature, as well as an MPI performance study.
Cleaning and stabilization method for dispersion strengthened materials produced from mechanically produced blends of metals plus oxide powders
Rigidly forced oscillatory dynamic stability method for measuring pitch and yaw damping derivatives in wind tunnels at transonic and supersonic speeds
Two proposed stabilization methods for X-15 horizontal surface control system