Framework Of Approximation Research Articles

Isovector and isoscalar spin-multipole giant resonances in the parent and daughter nuclei of double- β -decay triplets

The strength distributions, including giant resonances, of isovector and isoscalar spin-multipole transitions in the commonly studied double-$\ensuremath{\beta}$-decay triplets are computed in the framework of the quasiparticle random-phase approximation (QRPA) using the Bonn-$A$ two-body interaction in no-core single-particle valence spaces. The studied nuclei include the double-$\ensuremath{\beta}$ parent and daughter pairs ($^{76}\mathrm{Ge}$, $^{76}\mathrm{Se}$), ($^{82}\mathrm{Se}$, $^{82}\mathrm{Kr}$), ($^{96}\mathrm{Zr}$, $^{96}\mathrm{Mo}$), ($^{100}\mathrm{Mo}$, $^{100}\mathrm{Ru}$), ($^{116}\mathrm{Cd}$, $^{116}\mathrm{Sn}$), ($^{128}\mathrm{Te}$, $^{128}\mathrm{Xe}$), ($^{130}\mathrm{Te}$, $^{130}\mathrm{Xe}$), and ($^{136}\mathrm{Xe}$, $^{136}\mathrm{Ba}$). The studied transitions proceed from the ground states to the ${J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}},{1}^{\ensuremath{-}},{2}^{\ensuremath{-}}$ (spin-dipole transitions) and ${J}^{\ensuremath{\pi}}={1}^{+},{2}^{+},{3}^{+}$ (spin-quadrupole transitions) excited states in these nuclei. Comparison of the present results with potential future data may, indirectly, shed light on the reliability of QRPA-based nuclear-structure frameworks in description of the wave functions of nuclear states relevant for the two-neutrino and neutrinoless double $\ensuremath{\beta}$ decays in the studied triplets.

Accurate Field‐Effect Mobility and Threshold Voltage Estimation for Thin‐Film Transistors with Gate‐Voltage‐Dependent Mobility in Linear Region

AbstractThe measurement of mobility and threshold voltage in thin‐film transistors (TFTs) in which the mobility is a function of gate voltage or carrier density is usually done inaccurately. Herein, accurate mobility calculations within the framework of the gradual channel approximation are described. Conventionally, the derivative of drain current with respect to gate voltage is often used to calculate mobilities in the linear region. This procedure often leads to errors when the mobility is not constant. Using a first‐order finite difference‐based calculations, it is shown how the correct field‐effect mobility can be extracted. The corrected mobility can be smaller than the conventionally calculated field‐effect mobility by up to a factor of 2. It is also shown that the corrected field‐effect mobility is identical to the average mobility. A threshold voltage that is independent of gate voltage value and suitable for disordered semiconductors is used for more accurate mobility calculations. The mobility and threshold voltage calculations are illustrated with experimental data from multiple TFTs with indium gallium zinc oxide, zinc tin oxide, and molybdenum disulfide channel layers.

High-order corrections to the radiation-free dynamics of an electron in the strongly radiation-dominated regime

A system of reduced equations is proposed for electron motion in the strongly radiation-dominated regime for an arbitrary electromagnetic field configuration. The approach developed here is used to analyze various scenarios of electron dynamics in this regime: motion in rotating electric and magnetic fields and longitudinal acceleration in a plane wave and in a plasma wakefield. The results obtained show that this approach is able to describe features of electron dynamics that are essential in certain scenarios, but cannot be captured in the framework of the original radiation-free approximation [Samsonov et al., Phys. Rev. A 98, 053858 (2018) and A. Gonoskov and M. Marklund, Phys. Plasmas 25, 093109 (2018)]. The results are verified by numerical integration of the nonreduced equations of motion with account taken of radiation reaction in both semiclassical and fully quantum cases.

On the Quantum Confinement Effects in Ultrathin PdO Films by Experiment and Theory.

Radio frequency magnetron sputtering conducted in a high vacuum with a base pressure of 1×10-6 mbar was used to deposit ultrathin palladium films on Corning glass. The thickness of these films ranged from 0.4 to 13 nanometers. PdO films were produced after being post-annealed in a furnace at temperatures of 530 degrees Celsius in the presence of air. The results of an atomic force microscopy study showed that the material possessed a high crystalline quality with a low roughness. When looking at Tauc plots to determine the position of the direct optical band gap, the thicker films show a value that is relatively close to 2.2 eV. When the film thickness was reduced all the way down to 0.7 nm, a significant "blue shift" of more than 0.5 eV was observed. In order to provide a more in-depth understanding of the experiment, theoretical calculations based on the Hartree-Fock approximation as applied to an electron-hole system were performed in the framework of the effective mass approximation. The findings are regarded as empirical proof of the existence of quantum confinement effects.

Fused Microwave and Ultrasonic Breast Imaging Within the Framework of a Joint Variational Bayesian Approximation

Early diagnosis of breast tumors can, in principle, be achieved by jointly running electromagnetic and acoustic probings, more precisely microwave (MW) and ultrasound (US). Indeed, such modalities are noninvasive, nonionizing, and low cost and proceed without registration for free pending breasts, not like other joint modalities that impose compression. Because of the strongly contrasted electromagnetic parameters of breast constituents, MW yields high-contrast images of low resolution and converse with the US when faced with weakly refracting elements. The key benefit is the common breast structure, and fusion should produce images with both high contrast and resolution. A Bayesian formalism is chosen, and an unsupervised joint variational Bayesian approximation (JVBA) is developed. In that, edges’ hidden variables and hyperparameters are automatically tuned along with the optimization. The mathematics is detailed in a general setting of fusion, and then, one proposes imaging of realistic MRI-derived breast slices. A wealth of numerical simulations from noisy single-frequency MW and multiple-frequency US data preserved from inverse crime yields means (i.e., breast maps) and variances of the unknown electromagnetic and acoustic parameter distributions as probabilistic realizations, evolutions of hyperparameters, as well as global indicators of accuracy. Comparisons with a joint contrast-source inversion edge-preserving (JCSI-EP) developed earlier in a deterministic framework illustrate the methodology.

Attack Resilience of Cache Replacement Policies: A Study Based on TTL Approximation

Caches are pervasively used in communication networks to speed up content access by reusing previous communications, where various replacement policies are used to manage the cached contents. The replacement policy of a cache plays a key role in its performance, and is thus extensively engineered to achieve a high hit ratio in benign environments. However, some studies showed that a policy with a higher hit ratio in benign environments may be more vulnerable to cache pollution attacks that intentionally send requests for unpopular contents. To understand the cache performance under such attacks, we analyze a suite of representative replacement policies under the framework of TTL approximation in how well they preserve the hit ratios for legitimate users, while incorporating the delay for the cache to obtain a missing content. We further develop a scheme to adapt the cache replacement policy based on the perceived level of attack. Our analysis and validation on real traces show that although no single policy is resilient to all the attack strategies, suitably adapting the replacement policy can notably improve the attack resilience of the cache. Motivated by these results, we implement selected policies as well as policy adaptation in an open-source SDN switch to manage flow rule replacement, which is shown to notably improve its resilience to pollution attacks.

A Discrete-Time Framework for Designing Stable Digital V$^{2}$ Controllers for the Buck Converter

V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> control architecture is popular due to its simple compensation and fast load transient response. The stability margin of an analog V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> controlled buck converter improves as the input voltage or capacitor effective-series resistance (ESR) increases. However, due to voltage-loop sampling, stability margin of a digital V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> controlled buck converter degrades as the input voltage or capacitor ESR increases. Intuitively, it can be said that this happens due to sampling as sampling eliminates the ESR ripple from the output voltage. However, to get more clear insight and to propose a stabilizing solution, this article proposes an approximate discrete-time model-based framework. Analysis shows that the stability boundary of the controller's gain depends on the input and output voltages, and ESR. The stability boundary of the controller's gain is enhanced using an additional ramp compensation. Furthermore, a discrete-time small-signal model is developed to assess the slow-scale behavior of the buck converter. The model demonstrates an existence of complex conjugate poles with a low value of ESR. An analytical expression of critical value of ESR to keep the poles on the real axis is presented. To improve the load transient performance with a low ESR, a lag-lead compensator design technique is proposed. The proposed controller is realized in an FPGA device. Effectiveness of the proposed controller and accuracy of the analysis are validated experimentally.

Replacement and Repair Optimization for Production Systems Under Random Production Waits

This study considers a repairable production system operated under an age-based preventive replacement policy that is subject to independent random production waits and failures. In addition to the age-based replacement policy, we propose a maintenance model that uses production waits to schedule preventive replacement. That is, a decision maker can preventively replace the system either during a production wait or at the age threshold, whereas if a failure occurs during production, the decision maker must decide whether to perform a minimal repair or a corrective replacement to restore the system. Under the above setting, we develop a semi-Markov decision process (SMDP) to obtain the optimal maintenance policy that minimizes the long-run average maintenance cost rate. We establish the existence of the optimal maintenance policy and provide an algorithm to numerically obtain the optimal action for each state. We further generalize the model to incorporate imperfect maintenance and the nonhomogeneous arrival of production waits. In the latter case, it is computationally intractable to optimize the SMDP using a value iteration algorithm due to the curse of dimensionality. To address this challenge, we further develop an approximate dynamic programming framework to generate high-quality solutions. An attractive feature of our model is its generality, such that the model includes many existing maintenance models as special cases. A real-world example from a steel factory is used to demonstrate the proposed model.

Wannier-Mott excitons in alkali metal-based nitridorhenate: A DFT study

To better understand the electronic, structural, optical, and transport properties of the alkali metal-based nitridorhenate (Li 5 ReN 4 ), first-principles calculations were performed using the full potential linearized augmented plane wave (FP-LAPW) method within the generalised gradient approximation (GGA) framework. The ground-state properties were computed for an orthorhombic structure (Pmmn-59). Both the band structure and the total density of states were carried out. Based on the band structure, the Li 5 ReN 4 compound is a direct band semiconductor with a bandgap value of 2.68 eV. In addition, the optical properties were calculated, indicating that lithium nitridorhenate is a highly absorbent material. The effective masses of the electrons and holes were calculated. Also, we investigate the connection between exciton binding energy and band structure. Moreover, the exciton for Li 5 ReN 4 is a weak exciton of the Mott-Wannier type. Furthermore, the transport properties were investigated using the semi-classical Boltzmann theory as implemented in the BoltzTraP code. Owing to its semiconducting nature, the material has a high Seebeck coefficient (S) of 287 μV/K at 300 K. At 300 K and 400 K, the predicted thermoelectric figure of merit was 0.790 and 0.802. Each of these results shows that our compound is a strong choice for applications in photovoltaic, optoelectronic, and thermoelectrical devices. Additionally, based on the observation of thermoelectric figure of merit, the Li 5 ReN 4 compound is also suitable for waste heat regeneration or waste heat recovery process. The calculated charge density distribution of Li 5 ReN 4 along (011).

Transmit Beamforming for Ambient Backscatter Communication Enabled Wireless Body Area Network in Multiuser MISO System

Wireless Body Sensor Network (WBAN) is a promising technology which can provide pervasive E-health services. However, the power consumption of wireless communications in WBAN greatly restricts its applications. Recently Ambient Backscatter Communication (AmBC) technology has been introduced to realize ultra-low power passive wireless communication, thus it is highly desirable for WBAN. In this paper we consider that AmBC, powered by a multi-antenna Base Station (BS), is incorporated in WBAN to achieve ultra-low power intra-WABN communication. To fully exploit the potential of the AmBC in WBAN, the transmit beamforming at BS, the AmBC information symbol period as well as the transmission time allocation are jointly designed, taking into account Quality of Service (QoS) requirement of WBAN and cellular users, and BS power budget. The formulated optimization problem is highly nonconvex and very challenging to solve. To tackle this issue, we employ Inner Approximate (IA) framework to reformulate the original problem and solve it in an iterative manner. Finally, numerical results are provided to show the effectiveness of the proposed algorithm under various of system parameters settings.

Explicit Analytic Solutions for the Subsurface Stress Field in Single Plane Contacts of Elastically Similar Truncated Cylinders or Wedges

As has been pointed out recently, a possible solution strategy to the wear–fatigue dilemma in fretting, operating on the level of contact mechanics and profile geometries, can be the introduction of “soft” sharp edges to the contact profiles, for example, by truncating an originally smooth profile. In that regard, analysis of possible mechanical failure of a structure, due to the contact interaction, requires the knowledge of the full subsurface stress state resulting from the contact loading. In the present manuscript, a closed-form exact solution for the subsurface stress state is given for the frictional contact of elastically similar truncated cylinders or wedges, within the framework of the half-plane approximation and a local-global Amontons–Coulomb friction law. Moreover, a fast and robust semi-analytical method, based on the appropriate superposition of solutions for parabolic contact, is proposed for the determination of the subsurface stress fields in frictional plane contacts with more complex profile geometries, and compared with the exact solution. Based on the analytical solution, periodic tangential loading of a truncated cylinder is considered in detail, and important scalar characteristics of the stress state, like the von-Mises equivalent stress, maximum shear stress, and the largest principal stress, are determined. Positive (i.e., tensile) principal stresses only exist in the vicinity of the contact edge, away from the pressure singularity at the edge of the profile, and away from the maxima of the von-Mises equivalent stress, or the maximum shear stress. Therefore, the fretting contact should not be prone to fatigue crack initiation.

BullsEye : Scalable and Accurate Approximation Framework for Cache Miss Calculation

For Affine Control Programs or Static Control Programs (SCoP), symbolic counting of reuse distances could induce polynomials for each reuse pair. These polynomials along with cache capacity constraints lead to non-affine (semi-algebraic) sets; and counting these sets is considered to be a hard problem. The state-of-the-art methods use various exact enumeration techniques relying on existing cardinality algorithms that can efficiently count affine sets. We propose BullsEye , a novel, scalable, accurate, and problem-size independent approximation framework. It is an analytical cache model for fully associative caches with LRU replacement policy focusing on sampling and linearization of non-affine stack distance polynomials. First, we propose a simple domain sampling method that can improve the scalability of exact enumeration. Second, we propose linearization techniques relying on Handelman’s theorem and Bernstein’s representation . To improve the scalability of the Handelman’s theorem linearization technique, we propose template (Interval or Octagon) sub-polyhedral approximations. Our methods obtain significant compile-time improvements with high-accuracy when compared to HayStack on important polyhedral compilation kernels such as nussinov , cholesky , and adi from PolyBench , and harris , gaussianblur from LLVM -TestSuite. Overall, on PolyBench kernels, our methods show up to 3.31× (geomean) speedup with errors below ≈ 0.08% (geomean) for the octagon sub-polyhedral approximation.

Thermal equation of states for body-centered cubic tungsten using extended analytic embedded-atom model

Here the thermal equation of states (EOS) for body-centered cubic (bcc) tungsten (W) is evaluated using embedded atom method (EAM). To reproduce the materials properties under high pressure and high temperature reasonably well, we extend EAM by improving the analytic expressions of the functions of electron density and embedding energy based on the quantum-mechanical results of the electron density distribution and the energy variation with respect to the electron density. Then we determine the parameters of the extended analytic model for bcc W. We evaluate volume dependence of structure energy, elastic properties as function of volume, monovacancy and divacancy properties, lattice vibration at various volumes, and variation of the Gibbs free energy with respect to temperature, pressure and volume within the framework of the quasiharmonic approximation. By minimizing the Gibbs free energy, we determine the thermal EOS, variation of volume or lattice parameter with respect to pressure and temperature. The linear thermal expansion coefficient as function of temperature under different pressures is also evaluated. All calculation results fit well to the experimental and other reliable theoretical calculation results, showing the reliability of the extended analytic EAM in the extended domains of electron density, atomic volume, temperature and pressure.

A new framework for polynomial approximation to differential equations

In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework is based on an expansion of the vector field along an orthonormal basis, and relies on perturbation results for the considered problem. Initially devised for the approximation of ordinary differential equations, it is here further extended and, moreover, generalized to cope with constant delay differential equations. Relevant classes of Runge-Kutta methods can be derived within this framework.

Research on the Deep Learning Technology in the Hull Form Optimization Problem

A high−accuracy objective function evaluation method is crucial in ship hull form optimization. This study proposes a novel approximate ship hull form optimization framework using the deep learning technology, deep belief network algorithm. To illustrate the advantages of using the deep belief network algorithm in the prediction of total resistance, two traditional surrogate models (ELMAN and RBF neural networks) are also employed in this study to predict total resistance for different modified ship models. It can be seen from the results that the deep belief network algorithm is more suitable for forecasting total resistance of a DTMB5512 ship model than the traditional surrogate models. Following this, two design variables are selected to alter the bow geometry of the DTMB5512 ship model. The total resistance for different modified ship hulls is estimated using the deep belief network algorithm. Furthermore, an optimal solution with minimum total resistance in a two−dimensional space is obtained using the particle swarm optimization algorithm. The optimization results indicate that the optimization framework using the deep belief network algorithm can obtain an optimal solution with the smallest total resistance for different ship speeds.

Effects of applied magnetic field and pressure on the diamagnetic susceptibility and binding energy of donor impurity in GaAs quantum dot considering the non-parabolicity model’s influence

ABSTRACT In this article, we investigate the influence of the hydrostatic pressure, magnetic field, and conduction band non-parabolicity on both the diamagnetic susceptibility and the binding energy of shallow donor impurity in a quantum disk made out of GaAs. The Hamiltonian of the investigated problem has been solved within the framework of the effective-mass approximation. The energy minimisation has been performed using a variational approach. Our results reveal that both the diamagnetic susceptibility and binding energy have been reduced with increasing the disk size. Moreover, the diamagnetic susceptibility increases as the impurity moves from the extremity to the centre of the disk. However, both the diamagnetic susceptibility and binding energy have been improved under applied magnetic field, hydrostatic pressure, and by considering the conduction band non-parabolicity model as well. We hope that the reported results will be a modest contribution to further theoretical research in the field of nanostructures.

On the role of intermolecular vibrational motions for ice polymorphs. IV. Anisotropy in the thermal expansivity and the nonaffine deformation for ice IX and III.

We explore anisotropic properties in the thermal expansivities of hydrogen-ordered ice IX and its hydrogen-disordered counterpart, ice III. The free energies of these ice forms are calculated to obtain the lattice constants for the tetragonal unit cell and the thermal expansivities at various thermodynamic conditions in the framework of quasi-harmonic approximation, taking account of their anisotropic nature. The thermal expansivities are also examined by applying a thermodynamic relation that connects them with the Grüneisen parameters and the elastic compliances. Both calculations suggest that ice III and IX exhibit a negative thermal expansion along the a-axis but have a positive one along the c-axis at low temperatures. It is found that nonaffine deformation in the variation of the lattice constant beyond affine transformation (the Born approximation) is essential in the theoretical calculation of the thermal properties of ice III and IX. We also find that the nonaffine deformation is described by the shift of the minimum energy positions in the potential manifold of hydrogen-ordered ice along a limited number of the normal mode coordinates, which is irrelevant to the system size. These modes become unstable against an applied strain, so that the potential minimum moves along those normal coordinates away from that of the affine-transformed structure. The unstable modes are all symmetry-preserving modes, and the space-group symmetry is an invariant under displacement along either of those normal coordinates. The number of the unstable modes in ice IX is 8 while it is 1 in another hydrogen-ordered ice VIII.

Regulation of Continuum Harmonic Generation by Using Near-infrared Chirped Pulses

It has been known that the broadband of continuum harmonics, a regular periodicity or a wide smooth range, is essential for generating attosecond pulses. However, the high-order rescatterings of electrons (HOR) can significantly affect this important part of high-order harmonic spectra. In the present work, we apply the method suggested in our previous studies to limit the HOR effect on the continuum harmonics by using up-chirped pulses with frequency increasing in time to regulate the high-order harmonic generation of an asymmetric molecule such as CO subjected to a near-infrared laser. To do so, we numerically calculate the high-order harmonic spectra using the time-dependent wave functions obtained within the framework of the single-active electron approximation. To analyze and regulate the HOR effect, we use the time-frequency analysis together with the kinetic energy maps obtained from the equation of electron motion in the laser electric field. These techniques reveal the high-order harmonic dynamics, especially the effect of chirped pulse on the manifestation of continuum harmonics. Based on this, we release the notice on choosing appropriate parameters to obtain the optimal continuum range of harmonics. Although the detailed analysis is given for the CO molecule, the method suggested is applicable for other polar molecules.

Construction of an Analytical Solution of the Problem on the Formation of Gas Hydrate in a Porous Mine

In this paper, we propose the mathematical formulation of the problem on injection of a cold gas into a porous medium accompanied by the formation of gas hydrate. The mathematical formulation of the problem is an initial-boundary-value problem for a system of nonlinear partial differential equations expressing the laws of conservation of mass and energy supplemented by the conditions of mass and heat balance on the moving boundary of phase transitions. Within the framework of the rectilinear parallel approximation, we construct approximate analytical solutions with a temperature jump at the boundary where the gas hydrate appears. These solutions describe the relationship between the coordinate of the boundary of phase transition and the parameters of the injected gas and the porous medium.

URLLC Edge Networks With Joint Optimal User Association, Task Offloading and Resource Allocation: A Digital Twin Approach

This paper addresses the problem of minimising latency in computation offloading with digital twin (DT) wireless edge networks for industrial Internet-of-Things (IoT) environment via ultra-reliable and low latency communications (URLLC) links. The considered DT-aided edge networks provide a powerful computing framework to enable computation-intensive services, where the DT is used to model the computing capacity of edge servers and optimise the resource allocation of the entire system. The objective function is comprised of local processing latency, URLLC-based transmission latency and edge processing latency, subject to both communication and computation resources budgets. In this regard, the minimum latency is obtained by jointly optimising the transmit power, user association, offloading portions, the processing rate of users and edge servers. The formulated problem is highly complicated due to complex non-convex constraints and strong coupling variables. To deal with this computationally intractable problem, we propose an iterative algorithm which decomposes the original problem into three sub-problems and resolve this problem in the fashion of alternating optimisation approach combined with an inner convex approximation framework. Simulation results demonstrate the effectiveness of the proposed method in reducing the latency compared with other benchmark schemes.