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At least 1,675 records · Page 93

Solution of Periodic Boundary-Value Problems of the Spatial Theory of Elasticity in the Vector Form

We discuss boundary-value problems for the system of equations of the spatial theory of elasticity in the class of double-periodic functions and obtain a general solution of the system. We distinguish six types of elementary Floquet waves and examine their energy characteristics. We consider fundamental boundary-value problems in the half-space in the vector form. The diffraction problem for an elastic wave on a periodic system of defects in the vector form is reduced to the paired summator functional equation.

97 MATHEMATICS AND COMPUTING↗

The neutrino charge form-factor

Mathematical analysis and dispersion relations are used to obtain the general functional form of the neutrino charge form-factor. It is shown that if the scale for weak interactions is given by G, where G is the Fermi coupling constant, then for a large range of momentum transfer values, the form-factor may be approximated by a function that is linear in the square of the momentum transfer.

Mickens, R. E.↗

Computational design of high-entropy rare earth aluminum garnets for advanced thermal and environmental barrier coatings

To enhance the protection of Ni-based superalloys in gas turbine engines’ high-temperature environments, it’s crucial to develop advanced thermal/environmental barrier coating (T/EBC) materials with a balanced combination of thermal and mechanical properties. This optimization is essential to safeguard against chemical and thermal challenges. Here, in this study, we harness the power of density functional theory (DFT) in conjunction with combinatorial chemistry methodologies to engineer high-performance high-entropy rare earth disilicates of the RE 3 Al 5 O 12 family (where RE denotes Y, Gd, Er, and Yb). These materials are meticulously designed to exhibit superior phase stability, a targeted coefficient of thermal expansion (CTE), low lattice thermal conductivity, and robust mechanical properties. The determination of CTE values is accomplished through phonon calculations at various volume settings within the quasi-harmonic approximation, while lattice thermal conductivities are rigorously assessed employing the Debye-Callaway model, accounting for three distinct phonon processes. Our findings highlight the remarkable attributes of the solid solution (Y 1/4 Gd 1/4 Er 1/4 Yb 1/4 ) 3 Al 5 O 12 , which displays a reduction in lattice thermal conductivity compared to its individual constituents while maintaining a favorable range of CTE values. The novel T/EBC material, distinguished by their multifaceted functionalities, are poised to use in substantial enhancements in the performance of engines.

36 MATERIALS SCIENCE↗

Ultrasonic and optical evaluation of surgical implant materials and devices. A durability study of pericardial bioprostheses

Laser Doppler Anemometry (LDA) and accelerated fatigue testing were used in an attempt to assess the durability of two cardiac value bioprostheses. The LDA system was used to monitor the function of the cardiac valves over time. This was done through flow characterization in an aortic flow chamber, designed to closely simulate in vivo conditions, both in the near vicinity (sinuses of valsalva region) and also somewhat downstream (aortic region) from the values. The accelerated fatigue tester was operated by opening and closing the valves at a rate of 1300 R.P.M., about 18 x the normal rate. The results from the two test valves indicate a definite change in the flow characteristics downstream from the valve after certain accelerated test intervals. The high velocity cross-sectional flow area seems to increase over time in use, causing a decrease in the peak velocity. The tissue became more flaccid in certain areas, and tears were apparent at about 9.4 million cycles for the Ionescu-Shiley valve and at 24 million cycles for the Carpentier-Edwards valve. The use of Doppler ultrasound as a technique for monitoring the function of bioprostheses over time in vivo is also discussed.

Schuster, P. R.↗

Optimal Portfolio Management in a Modified Constant Elasticity of Variance Model

We investigate the optimal management of a portfolio consisting of a risk asset and a risk-free bond. The asset dynamics is specified by the M-CEV model. Assuming that the investor has a power utility function, we derive an explicit analytical portfolio-management formula that contains confluent hypergeometric functions. The asymptotic form of the proposed portfolio management strategy is obtained, as well as approximate formulas consisting only of elementary functions. We additionally present an application of our results in the context of algorithmic statistical-arbitrage strategies.

97 MATHEMATICS AND COMPUTING↗

Probabilistic Hazard Assessment for Tornadoes, Straight-Line Wind, and Extreme Precipitation at the Savannah River Site

Recent data sets for three meteorological phenomena with the potential to inflict damage on SRS facilities – tornadoes, straight-line winds, and heavy precipitation – are analyzed using appropriate statistical techniques to estimate the occurrence probabilities for these events in the future. Summaries of the results for DOE-mandated return periods and comparisons to similar calculations performed in 2013 by Werth et al. (W2013) are given. Using tornado statistics for i) the combined states of Georgia and South Carolina, and ii) a 2⁰ square area surrounding SRS, we calculated the probability per year of any location at SRS being struck by a tornado (the ‘strike’ probability) and the probability that any point will experience winds above set thresholds. The strike probability was calculated to be 7.04E-4 (1 chance in 1420) per year and tornadic wind speeds for DOE mandated return periods of 50,000 years (corresponding to wind design category 3 (WDC-3), and 125,000 years (meeting WDC-4) (USDOE, 2016) were estimated to be 132 mph and 147 mph, respectively. By contrast, default tornado wind speeds taken from ANSI/ANS-2.3-2011 are somewhat higher: 161 mph for return periods of 50,000 years and 173 mph every 125,000 years (ANS, 2011). Although the ANS and the SRS evaluation used the same basic model (Ramsdell and Rishel, 2007), the region defined in ANS 2.3 that encompasses the SRS also includes areas of the Great Plains and lower Midwest, regions with much higher occurrence frequencies of strong tornadoes. The SRS straight-line wind values associated with various return periods were calculated by fitting existing wind data to a GEV1 distribution and extrapolating the values for any return period from the tail of that function. For the DOE mandated return periods, we expect straight-line winds of 117 mph every 2500 years (the required WDC-3 standard) and 125 mph every 6250 years (WDC-4) at any point within the SRS. These values are similar to those from the ANS-2.3-2011 report, which has wind speeds of 125mph and 133 mph for return periods of 2500 years and 6250 years, respectively. For extreme precipitation, we compared the fits of two different theoretical extreme-value distributions and applied the one that fit the data best for each of several accumulation periods. The DOE mandated 6-hr accumulated rainfall for return periods of 10,000 years (corresponding to precipitation design category 3 (PDC-3) and 25,000 years (PDC-4) were estimated as 9.1 inches and 10.1 inches, respectively. For the 24-hr rainfall return periods of 10,000 years and 25,000 years, total rainfall estimates were 12.02 inches and 13.17 inches, respectively, higher than comparable values provided in the W2013 report.

54 ENVIRONMENTAL SCIENCES↗

Implementation and assessment of resolution-dependent elastic incoherent neutron scattering measurements at a backscattering spectrometer for probing relaxations in complex systems

We introduce the use of a higher-order reflection, Si(333), of the silicon analyzer crystals at a backscattering spectrometer to implement analysis of the relaxation dynamics in the samples. Here, this is achieved by monitoring the temperature dependence of the neutron scattering intensity perceived as elastic when measured using Si(111), Si(311), and Si(333) reflections. As a test case, we use a sample with well-characterized, but complex, relaxation pattern, where the non-Lorentzian relaxation function is known to exhibit a set of parameters specific to each temperature point and scattering momentum transfer (Q) value. Even for this very general relaxation pattern, characterized by no constrains on the relaxation function parameters, we successfully map the relaxation times measured using the present approach onto those previously obtained from the full analysis of the quasielastic neutron scattering signal. Analysis of the Q-specific activation energies becomes possible for the Q values accessible simultaneously through Si(111), Si(311), and Si(333) reflections (in the present case, 0.9 Å –1 < Q < 1.9 Å –1 ). While the dedicated neutron spectrometers for this type of analysis are yet to be constructed, we show that the present-day backscattering spectrometers can be employed, under certain conditions, to analyze temperature dependence of the relaxation time in the samples not amenable to traditional full analysis of the quasielastic neutron scattering signal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Accurate model of the stripe domain phase of perpendicularly magnetized multilayers

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value D thr beyond which the system is in a Néel state. We find that thicker films require larger values of DMI to stabilize the Néel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Furthermore our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.

36 MATERIALS SCIENCE↗

Nuclear Effects in the Deuteron in the Resonance and Deep-Inelastic Scattering Region

We discuss a model of the proton and neutron inelastic structure functions applicable in a wide region of the invariant mass W of produced hadronic states. The model relies on a hybrid approach, in which the scattering at sufficiently large values of W is described in terms of the parton distribution functions, while at low W we account for the contribution from the nucleon resonances. We apply the model to compute the deuteron structure function F{sub 2}{sup d} and perform systematic study of the ratios F{sub 2}{sup n}/ F{sub 2}{sup d} and (F{sub 2}{sup p}+F{sub 2}{sup n})/ F{sub 2}{sup d} for both, the deep-inelastic and the resonance, region in the context of recent measurements of BoNuS experiment at Jefferson Lab.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reconfigurable fuzzy cell

This invention relates to a reconfigurable fuzzy cell comprising a digital control programmable gain operation amplifier, an analog-to-digital converter, an electrically erasable PROM, and 8-bit counter and comparator, and supporting logic configured to achieve in real-time fuzzy systems high throughput, grade-of-membership or membership-value conversion of multi-input sensor data. The invention provides a flexible multiplexing-capable configuration, implemented entirely in hardware, for effectuating S-, Z-, and PI-membership functions or combinations thereof, based upon fuzzy logic level-set theory. A membership value table storing 'knowledge data' for each of S-, Z-, and PI-functions is contained within a nonvolatile memory for storing bits of membership and parametric information in a plurality of address spaces. Based upon parametric and control signals, analog sensor data is digitized and converted into grade-of-membership data. In situ learn and recognition modes of operation are also provided.

Salazar, George A.↗

Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Grain size strengthening, referred to as the Hall-Petch effect, is a common strategy to improve the yield strength of magnesium (Mg) alloys. Several experimental studies have reported that the Hall-Petch slope strongly depends on the texture of the alloy. This effect arises from altering grain boundaries (GBs) resistance to different slip systems to transfer across adjacent grains. The grain boundary barrier strength of certain grain boundaries to basal slip, referred to as basal micro-Hall-Petch, was investigated in the previous work. Here in this study, the micro-Hall-Petch coefficient values for the prismatic slip $(k^{prismatic}_{μ})$ in Mg-4Al and their correlation with the grain boundary parameters were investigated. An experimental method was developed to initiate the prismatic slip band at low-stress levels. High-resolution electron backscatter diffraction (HR-EBSD) was used to measure the residual stress tensor, from which the resolved shear stress ahead of blocked prismatic slip bands was computed for seven different grain boundaries. $(k^{prismatic}_{μ})$ values for each individual GB were calculated by coupling the stress profile information with a continuum dislocation pile-up model. The $(k^{prismatic}_{μ})$ values vary from 0.138 MPa.m 1/2 to 0.685 MPa. m 1/2 which are almost three times larger than the calculated values for the basal micro-Hall-Petch. The $(k^{prismatic}_{μ})$ values were correlated with the GB parameters, and a functional relationship depending on the two most effective angles, the angle between the traces of the slip planes on the GB plane ($\phi$) and the angle between incoming and outgoing slip directions (κ), was proposed to estimate the Hall-Petch barrier for prismatic slip system. The work provides coefficients that can be supplied as input to crystal plasticity models to couple the effect of texture and grain size effectively.

36 MATERIALS SCIENCE↗

Measurements of the Higgs boson production cross section in the four-lepton final state in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

The measurements of the Higgs boson (H) production cross sections performed by the CMS Collaboration in the four-lepton (4ℓ, ℓ = e, μ) final state at a center-of-mass energy $\sqrt{s}$ = 13.6 TeV are presented. These measurements are based on data collected with the CMS detector at the CERN LHC in 2022, corresponding to an integrated luminosity of 34.7 fb −1 . Cross sections are measured in a fiducial region closely matching the experimental acceptance, both inclusively and differentially, as a function of the transverse momentum and the absolute value of the rapidity of the four-lepton system. The H → ZZ → 4ℓ inclusive fiducial cross section is measured to be ${2.89}_{-0.49}^{+0.53}{\left({\text{stat}}\right)}_{-0.21}^{+0.29}\left({\text{syst}}\right)$ fb, in agreement with the standard model expectation of ${2.89}_{-0.49}^{+0.53}{\left({\text{stat}}\right)}_{-0.21}^{+0.29}\left({\text{syst}}\right)$ fb.

Higgs physics↗

Improved integrability and boundedness of solutions to some high-order variational problems

We give a series of results on the improved integrability and boundedness of solutions to several high-order variational problems with strengthened coercivity. In particular, we consider the homogeneous Dirichlet problem on the minimum of integral functionals and study variational inequalities with unilateral and bilateral obstacles and with integral and gradient constraints.

97 MATHEMATICS AND COMPUTING↗

Magnetized orbifolds and localized flux

Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an important ingredient of moduli stabilization. Flux quantization on orbifolds is subtle due to the orbifold singularities. Generically, Wilson line integrals around these singularities are non-trivial, which can be interpreted as localized flux. As a consequence, flux densities on orbifolds can take the same values as on tori. We determine the transition functions for the flux vector bundle on the orbifold T 2 /Z 2 and the related twisted boundary conditions of zero-mode wave functions. We also construct “untwisted” zero-mode functions that are obtained for singular vector fields related to the Green’s function on a torus, and we discuss the connection between zeros of the wave functions and localized flux. Twisted and untwisted zero-mode functions are related by a singular gauge transformation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.

42 ENGINEERING↗

Margins associated with loss of assured safety for systems with multiple weak links and strong links

Representations for margins associated with loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems involving multiple time-dependent failure modes are developed. Additionally, the following topics are described: (i) defining properties for WLs and SLs, (ii) background on cumulative distribution functions (CDFs) for link failure time, link property value at link failure, and time at which LOAS occurs, (iii) CDFs for failure time margins defined by (time at which SL system fails) - (time at which WL system fails), (iv) CDFs for SL system property values at LOAS, (v) CDFs for WL/SL property value margins defined by (property value at which SL system fails) - (property value at which WL system fails), and (vi) CDFs for SL property value margins defined by (property value of failing SL at time of SL system failure) - (property value of this SL at time of WL system failure). Included in this presentation is a demonstration of a verification strategy based on defining and approximating the indicated margin results with (i) procedures based on formal integral representations and associated quadrature approximations and (ii) procedures based on algorithms for sampling-based approximations.

42 ENGINEERING↗

Effect of the medium’s density on the hydrocyclonic separation of waste plastics with different densities

Highlights: • The density of medium is the key parameter to separate plastic particles. • The paper shows the theoretical analysis is in good agreement with test. • The optimum value of the medium’s density was obtained. • The optimum value of the medium’s density lies near that of denser particles. - Abstract: Hydrocyclones can be applied to recycle waste plastics with different densities through separating plastics based on their differences in densities. In the process, the medium density is one of key parameters and the value of the medium’s density is not just the average of the density of two kinds of plastics separated. Based on the force analysis and establishing the equation of motion of particles in the hydrocyclone, a formula to calculate the optimum separation medium density has been deduced. This value of the medium’s density is a function of various parameters including the diameter, density, radial position and tangential velocity of particles, and viscosity of the medium. Tests on the separation performance of the hydrocyclone has been conducted with PET and PVC particles. The theoretical result appeared to be in good agreement with experimental results.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Real-Time XANES Measurement of Se Reduction by Zerovalent Iron in a Flow-through Cell, and Accompanying Se Isotope Measurements

An anoxic flow-through cell experiment was conducted to examine mechanisms controlling the real-time reduction of selenate (Se(VI)) by zerovalent iron (ZVI), which is commonly used in permeable reactive barriers to treat dissolved contaminants including Se(VI). Changes in selenium (Se) isotope composition were examined by increasing the influent Se concentration over time, thus changing the proportion of Se removed from solution. At the conclusion of the experiment, an anoxic Se-free solution was pumped through the cell to assess the stability of the reaction products. At all stages, X-ray absorption data were obtained from the solid phase and Se isotope data from the aqueous phase. Reduced Se in the form of adsorbed Se(IV), Fe 2 SeO 4 , Se(0), and iron selenides accumulated on the ZVI over time. A linear regression function was fit to the $δ$ 82/76 Se values of the effluent, yielding an isotopic separation of 9.6‰. A Rayleigh curve was fit to the isotope data from the effluent samples collected during the rinse stage with an effective fractionation of 2.4‰. The results from this experiment can be used to elucidate the effect of multiple concurrent mechanisms on Se isotope behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗