Single State Research Articles

Methadone's Resurgence in Bridging the Treatment Gap in the Overdose Crisis: Position Statement of AMERSA, Inc (Association for Multidisciplinary Education, Research, Substance Use, and Addiction).

The United States is grappling with an unprecedented overdose crisis, exacerbated by the proliferation of potent synthetic opioids like illicitly manufactured fentanyl. Despite the efficacy of methadone treatment in managing opioid use disorder, regulatory barriers hinder its widespread utilization. This article examines the complex landscape of methadone regulation across federal, state, and local levels, highlighting disparities and opportunities for reform. The COVID-19 public health emergency prompted temporary flexibility in methadone regulations, including expanded take-home doses and telehealth counseling, leading to improved treatment experiences and retention. Permanent revisions to federal guidelines have since been introduced by the Substance Abuse and Mental Health Services Administration, reflecting a progressive shift toward patient-centered care and streamlined access. State regulations, managed by Single State Agencies and State Opioid Treatment Authorities, vary widely, often imposing additional restrictions that impede access to methadone treatment. Local OTP clinics further exacerbate barriers through stringent policies, despite federal and state guidelines advocating for flexibility. Coordinated efforts among policymakers, healthcare providers, and communities are needed to promote the development of accountability measures, incentives, and community involvement to ensure equitable access and quality of care. To truly meet the demand needed to end the existing overdose crisis and enhance accessibility and comprehensive healthcare services, methadone treatment expansion beyond traditional OTP settings into primary care offices and community pharmacies should take place.

Label-Free Three-Dimensional Morphological Characterization of Cell Death Using Holographic Tomography.

This study presents a novel label-free approach for characterizing cell death states, eliminating the need for complex molecular labeling that may yield artificial or ambiguous results due to technical limitations in microscope resolution. The proposed holographic tomography technique offers a label-free avenue for capturing precise three-dimensional (3D) refractive index morphologies of cells and directly analyzing cellular parameters like area, height, volume, and nucleus/cytoplasm ratio within the 3D cellular model. We showcase holographic tomography results illustrating various cell death types and elucidate distinctive refractive index correlations with specific cell morphologies complemented by biochemical assays to verify cell death states. These findings hold promise for advancing in situ single cell state identification and diagnosis applications.

Deterministic preparation of optical qubits with coherent feedback control

We propose a class of preparation schemes for orbital angular momentum and polarization qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarization state onto a two-level OAM system (swap) for arbitrary OAM values ±ℓ within a light beam, i.e., without a spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. The swap scheme also allows us to implement arbitrary unitary gates on OAM qubits (±ℓ) by reducing them to polarization gates. In addition, we show how to translate measurement-based qubit control channels into coherent feedback schemes for optical implementation.

Cavity QED systems for steady-state sources of Wigner-negative light

We present a theoretical investigation of optical cavity quantum electrodynamics (cavity QED) systems, as described by the driven, open Jaynes–Cummings model and some of its variants, as potential sources of steady-state Wigner-negative light. We consider temporal modes in the continuous output field from the cavity and demonstrate pronounced negativity in their Wigner distributions for experimentally relevant parameter regimes. We consider models of both single and collective atomic spin systems, and find a rich structure of Wigner-distribution negativity as the spin size is varied. We also demonstrate an effective realization of all of the models considered using just a single 87Rb atom and based upon combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state.

Revealing the Role of Spacer Layer in Domain Dynamics of Hf0.5Zr0.5O2 Thin Films for Ferroelectrics

AbstractHfO2‐based ferroelectrics offer promises for next‐generation nonvolatile nanoscale devices owing to excellent CMOS compatibility and robust ferroelectricity at the nanoscale. However, fundamentally understanding the mechanism of polarization reversal and domain dynamics is challenging because the role of the spacer layer at the domain level in HfO2‐based ferroelectrics remains elusive. Here, it is realized that visualization of time‐resolved dynamics of nanoscale domain configurations in the epitaxial Hf0.5Zr0.5O2 thin films using phase‐field simulations. Scale‐free domain independent switchability (namely, irreducible stable polar domain down to 1 nm lateral size) and sharp domain walls that originate from weak interactions between adjacent domains characterized by the reduced gradient energy coefficient, which unravels the mesoscale mechanism of spacer layer in domain dynamics are demonstrated. Meanwhile, it is revealed that 180° polarization switching is dominated by the nucleation of a new domain with a high nucleation density, well described by the nucleation‐limited switching model. This study not only provides a fundamental mesoscale mechanism of the spacer layer, but also stimulates further studies on the manipulation of ultra‐scaled single domain state for designing high‐density and fast‐speed HfO2‐based ferroelectric memory.

Maximising CP Violation in naturally aligned Two-Higgs Doublet Models

The Two-Higgs Doublet Model (2HDM) is a well-motivated theoretical framework that provides additional sources of CP Violation (CPV) beyond the Standard Model (SM). After studying the vacuum topology of a general (convex) 2HDM potential, we unambiguously identify three origins of CPV: (i) Spontaneous CPV (SCPV), where the vacuum manifold has at least two degenerate CPV minima disconnected by domain walls, (ii) Explicit CPV (ECPV) with one single CPV ground state, and (iii) Mixed Spontaneous and Explicit CPV (MCPV), where the theory possesses more than one non-degenerate CPV local minimum. Most importantly, we define a novel complex parameter rCP whose norm and phase control the three different realisations of CPV, at least at the tree level. In all these scenarios, only two CPV phases can be made independent, as any third CPV parameter will always be constrained via the CP-odd tadpole condition. Since ECPV vanishes in 2HDMs where SM Higgs alignment is achieved naturally through accidental continuous symmetries, we analyse the possibility of maximising CPV through soft and explicit breaking of these symmetries. We derive upper limits on key CPV parameters that quantify the degree of SM misalignment from constraints due to the non-observation of an electron Electric Dipole Moment (EDM). Finally, we delineate the CP-violating parameter space of the so-constrained naturally aligned 2HDMs that can further be probed at the CERN Large Hadron Collider (LHC).

Engineering complete delocalization of single particle states in a class of one dimensional aperiodic lattices: A quantum dynamical study

We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of any translational periodicity. The chosen lattices are stubbed with one or more atoms, tunnel coupled to the backbone, thereby introducing a minimal quasi-one dimensionality. It is seen that, for a group of such lattices a certain correlation between the numerical values of the hopping amplitudes leads to a complete delocalization of single particle states. In some other cases, a special value of a magnetic flux trapped in the loops present in the geometries delocalize the states, leading to a flux driven insulator to metal transition. The mean square displacement, temporal autocorrelation function, the time dependence of the inverse participation ratio, or the information entropy – the so-called hallmarks of studying localization based on dynamics – all of them indicate such a complete turnover in the nature of the single particle states and the character of the energy spectrum under suitable conditions. The results shown in this work using quasiperiodic lattices of the Fibonacci family are much more general and hold good even for a randomly disordered arrangement of the building blocks of the systems considered, and indicate a subtle universality class under which these lattices can be grouped.

Some Aspects of Maxwell’s Equations, Klein-Gordon Equations, and Heat and Mass Transfer Equations in an n-Dimensional Maximally Symmetric Space-Time from the Classical and Quantum Mechanical Standpoints

This manuscript examines Maxwell’s equations, Klein-Gordon equations, and heat and mass transfer equations in n-dimensional maximally symmetric space-time. It investigates these equations in spherical and hyperbolic spaces embedded in higher-dimensional Euclidean and Minkowski spaces. The study focuses on the implications of these geometries and symmetries on the behaviour of the equations, highlighting how specific transformations and parametrizations impact their solutions. The findings reveal the underlying connections between geometric symmetries and physical laws, providing insights into their possible applications in theoretical physics. We touch upon both classical and quantum mechanical aspects of density and velocity evolutions with time in the universe. Quantum mechanical aspects of single and two-particle state evolution and statistical moments of the matter four-current are derived from the quantum Boltzmann equation and Feynman’s path integral method for fields applied to gravity interacting with electrons and positrons.

Historical and legal characteristics of the Act of Unity of the Ukrainian People’s Republic and the Western Ukrainian People’s Republic and its state-building potential

The article is devoted to the study of the prerequisites and procedural aspects of the conclusion of the Act of Unity of the Ukrainian People’s Republic and the Western Ukrainian People’s Republic on January 22, 1919, which was the culmination of centuries-old efforts of Ukrainians to unite their historical national lands within the boundaries of a single sovereign and independent state of Ukraine. The process of affirming the unity of the Ukrainian lands historically began with the search for support for the Western Ukrainian People’s Republic among the political elites of Trans-Dnieper Ukraine. The pre-accession agreement concluded between representatives of the Western Ukrainian political elite and the newly formed Directorate of the Ukrainian People’s Republic provided for the procedure for ratifying the union of the two parts of Ukraine. The aspirations of Western Ukrainian People’s Republic representatives regarding equal representation in the highest bodies of state administration, which they previously discussed with the Management, were not realized. In fact, the Directory recognizes the autonomous status of Western Ukrainian People’s Republic as one of the regions of Ukraine under the name Western Region of the Ukrainian People’s Republic. The management of the Directory was aware of the declarative nature of the connection. The paradigm of the historical perspective and parallels through the centuries brings us back to the need to constantly study the strengths and positive experiences of the past, study mistakes in order to avoid them in the future. The period of Ukrainian national development studied in the article went through many difficult trials, but this encouraged Ukrainians to raise national liberation ideas to a new level - awareness of the need for national and territorial unity. The leaders of the Ukrainian People’s Republic and Western Ukrainian People’s Republic failed to realize the positive aspirations that were laid down in their positive movement towards the unity of the state. The main drawback was that the main institutions of power of the Ukrainian People’s Republic remained formed according to the imperial model. There was a lack of professional and at the same time nationally conscious personnel. An important historical experience of the relationship between the two parts of Ukraine, which must be taken into account in the current conditions of Ukraine, is the development of a common national policy, the vector of which is national interests, sovereignty and protection of the independence and territorial integrity of the state.

(2S,4S)-5-Fluoroleucine, (2S,4R)-5-Fluoroleucine, and 5,5'-Difluoroleucine in Escherichia coli PpiB: Protein Production, 19F NMR, and Ligand Sensing Enhanced by the γ-Gauche Effect.

Global substitution of leucine for analogues containing CH2F instead of methyl groups delivers proteins with multiple sites for monitoring by 19F nuclear magnetic resonance (NMR) spectroscopy. The 19 kDa Escherichia coli peptidyl-prolyl cis-trans isomerase B (PpiB) was prepared with uniform high-level substitution of leucine by (2S,4S)-5-fluoroleucine, (2S,4R)-5-fluoroleucine, or 5,5'-difluoroleucine. The stability of the samples toward thermal denaturation was little altered compared to the wild-type protein. 19F nuclear magnetic resonance (NMR) spectra showed large chemical shift dispersions between 6 and 17 ppm. The 19F chemical shifts correlate with the three-bond 1H-19F couplings (3JHF), providing the first experimental verification of the γ-gauche effect predicted by [Feeney, J. J. Am. Chem. Soc. 1996, 118, 8700-8706] and establishing the effect as the predominant determinant of the 19F chemical shifts of CH2F groups. Individual CH2F groups can be confined to single rotameric states by the protein environment, but most CH2F groups exchange between different rotamers at a rate that is fast on the NMR chemical shift scale. Interactions between fluorine atoms in 5,5'-difluoroleucine bias the CH2F rotamers in agreement with results obtained previously for 1,3-difluoropropane. The sensitivity of the 19F chemical shift to the rotameric state of the CH2F groups potentially renders them particularly sensitive for detecting allosteric effects.

CryoEM-sampling of metastable conformations appearing in cofactor-ligand association and catalysis of glutamate dehydrogenase

Kinetic aspects of enzymatic reactions are described by equations based on the Michaelis–Menten theory for the initial stage. However, the kinetic parameters provide little information on the atomic mechanism of the reaction. In this study, we analyzed structures of glutamate dehydrogenase in the initial and steady stages of the reaction using cryoEM at near-atomic resolution. In the initial stage, four metastable conformations displayed different domain motions and cofactor/ligand association modes. The most striking finding was that the enzyme-cofactor-substrate complex, treated as a single state in the enzyme kinetic theory, comprised at least three different metastable conformations. In the steady stage, seven conformations, including derivatives from the four conformations in the initial stage, made the reaction pathway complicated. Based on the visualized conformations, we discussed stage-dependent pathways to illustrate the dynamics of the enzyme in action.

Regularity of the Optimal Sets for a Class of Integral Shape Functionals

We prove the first regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} is obtained as the integral of a cost function j(u, x) depending on the solution u of a certain PDE problem on Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}. The main feature of these functionals is that the minimality of a domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} cannot be translated into a variational problem for a single (real or vector valued) state function. In this paper we focus on the case of affine cost functions j(u,x)=-g(x)u+Q(x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j(u,x)=-g(x)u+Q(x)$$\\end{document}, where u is the solution of the PDE -Δu=f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\Delta u=f$$\\end{document} with Dirichlet boundary conditions. We obtain the Lipschitz continuity and the non-degeneracy of the optimal u from the inwards/outwards optimality of Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} and then we use the stability of Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} with respect to variations with smooth vector fields in order to study the blow-up limits of the state function u. By performing a triple consecutive blow-up, we prove the existence of blow-up sequences converging to homogeneous stable solution of the one-phase Bernoulli problem and according to the blow-up limits, we decompose ∂Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Omega $$\\end{document} into a singular and a regular part. In order to estimate the Hausdorff dimension of the singular set of ∂Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Omega $$\\end{document} we give a new formulation of the notion of stability for the one-phase problem, which is preserved under blow-up limits and allows to develop a dimension reduction principle. Finally, by combining a higher order Boundary Harnack principle and a viscosity approach, we prove C∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^\\infty $$\\end{document} regularity of the regular part of the free boundary when the data are smooth.

Impact of annealing on Cu2O doped with Na/Co: Structural, optical, and electrochemical consequences

Impact of annealing on Cu2O doped with Na/Co: Structural, optical, and electrochemical consequences

Synthesis of Perylene Diimide Modified by POSS and its Assembly Behavior in Solution and SBS Matrix

In this work, Perylene diimide derivatives 1,7- POSS-PDI-C12 (PPC) were synthesized using 1,7-Br-PDI- C12, 18-crown-6 ether as phase transfer agent, K2CO3 as catalyst and THF as solvent in a reaction system. Subsequently, the POSS-SH group was successfully introduced into the perylene imide bay site in high yield. The chemical structure and molecular weight of the products were characterized by 1H-NMR, 13C-NMR, MALDI-TOF MS and FT-IR. The self-assembly behavior in different solvents was studied using the research solution self-assembly method. PPC remained in a single monomolecular state due to the bulky POSS group, which introduced large steric hindrance in the molecular packing, leading to the weakening of the π–π interactions. Then, the Composite thin films containing PPC in SBS was prepared. PPC do not exhibit significant force-chromic behavior owing to the dispersion of single- molecule states. This shows that in the construction of mechanochromic materials, chromophore molecules need to have a certain degree of aggregation in the matrix, but the aggregation degree should not be too high.

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

Transforming waste into valuables: Preparation and evaluation of dual-ligand hydrophobic charge-induction chromatography using two poor performing ligands

In conventional chromatographic ligand screening, underperforming ligands are often dismissed. However, this practice may inadvertently overlook potential opportunities. This study aims to investigate whether these underperforming ligands can be repurposed as valuable assets. Hydrophobic charge-induction chromatography (HCIC) is chosen as the validation target for its potential as an innovative chromatographic mode. A novel dual-ligand approach is employed, combining two suboptimal ligands (5-Aminobenzimidazole and Tryptamine) to explore enhanced performance and optimization prospects. Various dual-ligand HCIC resins with different ligand densities were synthesized by adjusting the ligand ratio and concentration. The resins were characterized to assess appearance, functional groups, and pore features using SEM, FTIR, and ISEC techniques. Performance assessments were conducted using single-ligand mode resins as controls, evaluating the selectivity against human immunoglobulin G and human serum albumin. Static adsorption experiments were performed to understand pH and salt influence on adsorption. Breakthrough experiments were conducted to assess dynamic adsorption capacity of the novel resin. Finally, chromatographic separation using human serum was performed to evaluate the purity and yield of the resin. Results indicated that the dual-ligand HCIC resin designed for human antibodies demonstrates exceptional selectivity, surpassing not only single ligand states but also outperforming certain high-performing ligand types, particularly under specific salt and pH conditions. Ultimately, a high yield of 83.9 % and purity of 96.7 % were achieved in the separation of hIgG from human serum with the dual-ligand HCIC, significantly superior to the single-ligand resins. In conclusion, through rational design and proper operational conditions, the dual-ligand mode can revitalize underutilized ligands, potentially introducing novel and promising chromatographic modes.

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Multiple conformational states assembly of multidomain proteins using evolutionary algorithm based on structural analogues and sequential homologues

With the breakthrough of AlphaFold2, nearly all single-domain protein structures can be built at experimental resolution. However, accurate modelling of full-chain structures of multidomain proteins, particularly all relevant conformations for those with multiple states remain challenging. In this study, we develop a multidomain protein assembly method, M-SADA, for assembling multiple conformational states. In M-SADA, a multiple population-based evolutionary algorithm is proposed to sample multiple conformational states under the guidance of multiple energy functions constructed by combining homologous and analogous templates with inter-domain distances predicted by deep learning. On a developed benchmark dataset containing 72 multidomain proteins with multiple conformational states, the performance of M-SADA is significantly better than that of AlphaFold2 on multiple conformational states modelling, where 29/72 (40.3%) of proteins can be assembled with a TM-score > 0.90 for two highly distinct conformational states with M-SADA. Furthermore, M-SADA is tested on a developed benchmark dataset containing 296 multidomain proteins with single conformational state, and results show that the average TM-score of M-SADA on the best models is 0.913, which is 5.2% higher than that of AlphaFold2 models (0.868). Results on CASP15 multidomain targets also show that M-SADA can predict new domain arrangements when individual domain structures are correct.

Modeling of tungsten impurity transport and distribution in EAST based on multi-fluid and kinetic Monte Carlo simulations

In recent years, the materials of plasma facing components, such as divertor target plates, domes, and outer walls of tokamaks, such as ASDEX Upgrade, WEST, JET, EAST, and ITER, have been changed from carbon to tungsten because of its lower erosion and tritium retention rates. Impurities are produced by interactions between the plasma and the first wall. This study provides an investigation to simulate the transport and distribution of tungsten impurities in the edge plasma on EAST. The 2D multi-fluid edge plasma transport code SOLPS-ITER and 2D kinetic Monte Carlo impurity transport code DIVIMP were used in the simulations. The multi-fluid model in SOLPS-ITER and the kinetic Monte Carlo model in DIVIMP were employed to treat tungsten impurity ions. The 2D density contour distributions in the computational region and the 1D density radial profiles at the inner and outer midplanes of tungsten impurity particles with ionization states (W0–W+74) and the total tungsten particles with all charge states were obtained. With the heating power 1.5 MW and the line-averaged plasma density 2 × 1019 m−3, the results from SOLPS-ITER and DIVIMP show that the maximum density of tungsten ion with single ionization state is about 1014 m−3 and the total density of tungsten impurities with all charge states is about 1015 m−3 at the core boundary. To the best of our knowledge, the simulation results from SOLPS-ITER and DIVIMP are compared for the first time to benchmark SOLPS-ITER with the multi-fluid mode and DIVIMP with the kinetic model for tungsten impurity transport. The density distributions of tungsten impurities with different ionization states from SOLPS-ITER and DIVIMP are highly similar, and good agreement can be found under similar conditions involved in the calculation. From the comparison benchmark between SOLPS-ITER and DIVIMP for tungsten impurity transport, it can be concluded that the impurity transport approximation used by DIVIMP is good.

Optimal design of elastic plates

This paper is concerned with optimal design problems in the setting of the Kirchhoff–Love model for pure bending of a thin solid symmetric plate under a transverse load. For two isotropic elastic materials with a prescribed amount, the goal is to find their rearrangement within the domain that forms a least compliant structure. The homogenization method is used as a relaxation tool to overcome the lack of a classical solution of optimal design problem. Neccessary conditions of optimality were derived and an optimality criteria method for the single state compliance minimization problems is developed and tested on several examples.