Intrinsic Volume Research Articles

An intrinsic volume metric for the class of convex bodies in ℝn

A new intrinsic volume metric is introduced for the class of convex bodies in [Formula: see text]. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a restricted number of vertices under this metric. This result improves the best known estimate, and shows that dropping the restriction that the polytope is contained in the ball or vice versa improves the estimate by at least a factor of dimension. The same phenomenon has already been observed in the special cases of volume, surface area and mean width approximation of the ball.

Vacancies-mediated atomic diffusion controlled by the interfacial structure of FCC/BCC HEA multilayers

The radiation-induced segregation is one of the major concerns for nuclear materials, as it can damage the service performance of the material. Eutectic high entropy alloy (HEA) multilayer is considered a potential nuclear material for improving the irradiation tolerance of materials, due to its outstanding irradiation tolerance and mechanical properties. Abundant heterogeneous interfaces in eutectic HEA multilayer can interact with irradiation-induced vacancies, thus resulting in changes in the behavior of atomic diffusion and segregation. In the current work, to explore the effects of the heterogeneous interfacial structure on atomic diffusion and segregation, we have investigated the evolution of the elemental distribution in FCC/BCC HEA multilayers with coherent and semicoherent interfaces under vacancy flow in detail. It is found that the segregation and atomic diffusion behaviors of eutectic HEA multilayer are sensitive to the heterogeneous interfacial structure. The semicoherent interface promotes the interface diffusion and interface segregation due to the vacancy annihilation at interface and the intrinsic excess volume of interface. Whereas, the coherent interface is benifcial to the intragranular diffusion because it is transparent for the diffusion of vacancy.

MoSe2 Complex with N and B Dual-Doped 3D Carbon Nanofibers for Sodium Batteries

The sodium battery is one of the best energy storage technologies due to its abundant resource reserves and excellent energy storage ability. As a two-dimensional layered transition metal, molybdenum selenide (MoSe2) has large interlayer spacing and a high theoretical capacity (470 mAh∙g−1). Its structure is suitable for the negative electrode of sodium-ion batteries, with a large ionic radius and slow ion diffusion kinetics. However, it is difficult for the rate capability and cycling performance of MoSe2 to meet practical needs due to a weak intrinsic electron transport ability and volume expansion during sodium absorption. The hydrothermal synthesis method was used to synthesize the MoSe2 complex based on boron and nitrogen dual-doped 3D carbon fibers obtained from bacterial cellulose membranes (MoSe2/N&B-BCM) for sodium batteries. Additionally, electrochemical analysis and experimental characterization were performed. In summary, the experimental analysis shows that MoSe2/N&B-BCM has excellent conductivity, structural integrity, cyclability (328 mAh∙g−1 after 100 cycles at a 0.5 c constant rate), and rate stability.

Generalizable Synthesis of Highly Fluorinated Ionic Liquids.

The unique chemistry of fluorocarbons (in particular, their weak intermolecular interactions and high degree of intrinsic free volume) makes them promising building blocks for ionic liquids with high gas capacities. Here, we report a generalizable method for the synthesis of fluorinated ionic liquids, which relies on the evolution of gaseous byproducts to drive product formation. This synthetic strategy overcomes solubility challenges that can hinder the synthesis of highly fluorinated ionic liquids via conventional methods and enables a systematic investigation of the effect of fluorination on ionic liquid viscosity and gas solubility.

Intrathoracic negative pressure therapy of pleural empyema using an open-pored drainage film

We report our initial experience with intrathoracic negative pressure therapy (ITNPT) in the stage-adjusted therapy of pleural empyema (PE) based on a case series. ITNPT represents a further development in negative pressure therapy that is designed to be used in the thoracic cavity. After thoracic surgical open debridement, an intrathoracic negative pressure dressing was inserted. The drainage elements used were a thin open-pore double-layer drainage film (OF) with open-pore polyurethane foams (PUF). Only the OF was placed in direct contact with the lung parenchyma. Negative pressure was generated using an electronic pump (continuous suction, -75 mm Hg). In revision thoracotomies, ITNPT was stopped or continued depending on local findings. 31patients with stageII and III pleural empyemas were treated. ITNPT was administered at the time of primary procedure (n = 17) or revision (n = 14). ITNPT was given over a duration of m = 10 days (2-18days), change interval m = 4d (2-6d). The application of intrathoracic negative pressure dressings was performed m = 3.5 (1-6) times. The empyema cavity continuously reduced in size and was cleansed by the suction. The OF has a minimum intrinsic volume with maximum absorption surface. Once negative pressure is established, there is no intrathoracic dead volume and the parenchyma can expand. The protective material properties of OF make ITNPT suitable for the treatment of pleural empyema. Targeted local intrathoracic drainage of the septic focus is a possible adjunct to surgery. The treatment regimen requires surgical dressings to be changed repeatedly. The method is suitable for the treatment of complex stage II and III pleural empyemas. The OF can be used as an intrathoracic drainage element for ITNPT in pleural empyema. This new application option expands the range of indications for negative pressure therapy.

Bilayer Dense-Porous Li7 La3 Zr2 O12 Membranes for High-Performance Li-Garnet Solid-State Batteries.

Li dendrites form in Li7 La3 Zr2 O12 (LLZO) solid electrolytes due to intrinsic volume changes of Li and the appearance of voids at the Li metal/LLZO interface. Bilayer dense-porous LLZO membranes make for a compelling solution of this pertinent challenge in the field of Li-garnet solid-state batteries (SSB). Lithium is thus stored in the pores of the LLZO, thereby avoiding i) dynamic changes of the anode volume and ii) the formation of voids during Li stripping due to increased surface area of the Li/LLZO interface. The dense layer then additionally reduces the probability of short circuits during cell charging. In this work, a method for producing such bilayer membranes utilizing sequential tape-casting of porous and dense layers is reported. The minimum attainable thicknesses are 8-10µm for dense and 32-35µm for porous layers, enabling gravimetric and volumetric energy densities of Li-garnet SSBs of 279Wh kg-1 and 1003Wh L-1 , respectively. Bilayer LLZO membranes in symmetrical cell configuration exhibit high critical current density up to 6mA cm-2 and cycling stability of over 160 cycles at a current density of 0.5mA cm-2 at an areal capacity limitation of 0.25 mAh cm-2 .

Stable anisotropic minimal hypersurfaces in

AbstractWe show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in$\mathbf {R}^4$has intrinsic cubic volume growth, provided the parametric elliptic integral is$C^2$-close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in$\mathbf {R}^4$. The new proof is more closely related to techniques from the study of strictly positive scalar curvature.

Giant negative thermal expansion in Zn2-Cu P2O7 ceramics via microstructure effect

As a novel thermophysical behavior, negative thermal expansion (NTE) has been studied in many materials. However, rare materials have realized giant NTE, and the methods to improve NTE are lacking. Herein, a giant NTE has been achieved in Zn 2- x Cu x P 2 O 7 ceramics via microstructure effect. In the Zn 1.96 Cu 0.04 P 2 O 7 ceramic body, the linear contraction measured by dilatometry reaches to 0.9% (3ΔL/L = 2.7%) when heated from −30 °C to 125 °C, while the intrinsic crystallographic volume contraction derived by X-ray diffraction is only 1.68%. The remarkable NTE enhancement in the ceramic sample is attributed to the microstructure effect. An apparent shrinkage of the voids has been observed by in-situ atomic force microscope (AFM). The voids with large size in the ceramic body is the key factor to enhance NTE. This is the first time to observe direct experimental evidence by AFM for microstructure effect. Microstructure effect is an effective method to produce giant NTE.

Growth Mechanism and Synchronization Effect of China’s New Energy Vehicle Enterprises: An Empirical Analysis Based on Moving Logistic and Kuramoto Model

The primary purpose of this paper is to discuss whether NEV enterprises can achieve synchronous effects with the whole Chinese automobile industry in terms of growth mode. In this paper, we study the development of new energy vehicles from the perspective of ecosystem. Growth mechanisms and synchronization effects also exist in new energy enterprise populations, just like biological populations in natural ecosystems. Here, we propose a moving logistic model to analyze the growth mechanism of new energy vehicle enterprises and obtain serial data of intrinsic growth rate, internal inhibition coefficient, and theoretical maximum sales volume. The intrinsic growth rate and theoretical maximum sales volume show an initial trend of decline followed by recovery. The evaluation results of coupling degree and synchronization of the new energy vehicle population were obtained through the measurement of the Kuramoto model and its derivative model. The coupling degree of the new energy vehicle population is not high, and the synchronization effect fluctuates and oscillates. The change trend of synchronization effect is similar to that of intrinsic growth rate and theoretical maximum sales volume. This phenomenon shows that the new energy vehicle population has been significantly affected by changes in the external market environment. The analysis method of enterprise growth mechanism based on the moving logistic model and the measurement method of coupling degree and synchronization effect based on the Kuramoto model and its derivative models proposed in this paper effectively achieve the research objectives of this paper.

Constructing Three-Dimensional Topological Zn Deposition for Long-Life Aqueous Zn-Ion Batteries.

Uniform and compact Zn deposition-dissolution is essential to achieve high Coulombic efficiency and long lifespan for Zn anodes. More attention has been commonly focused on the suppression of macroscopic Zn dendrites in the previous reports. The rational control of the microstructure of Zn deposition to prevent the intrinsic volume expansion and pulverization of Zn metal so as to stabilize Zn anodes is less discussed. Herein, we construct a three-dimensional topological Zn deposition at the nanoscale through an in situ electrochemical process in the optimal hybrid aqueous electrolyte. The topological electrode structure can efficiently accommodate microscopic strain and volume variation and thus largely preserve the macroscopic integrity and electrical contact of Zn anodes, leading to enhanced reversibility and stability. With the unique topological structure of Zn deposition, the Coulombic efficiency of Zn anodes could reach >99.9% with excellent cycling over 1182 h at 2 mA cm-2 and 2 mA h cm-2 (Zn utilization: 11.4%). The evolution of "dead" Zn during repeated cycling is first investigated using a homemade semiquantitative analysis method to determine the critical "short slab" for aqueous Zn batteries under the practical application. This work provides an insightful method to regulate the microscopic morphology of Zn deposition for high-performance Zn batteries.

Accuracy and repeatability of joint sparsity multi-component estimation in MR Fingerprinting

MR fingerprinting (MRF) is a promising method for quantitative characterization of tissues. Often, voxel-wise measurements are made, assuming a single tissue-type per voxel. Alternatively, the Sparsity Promoting Iterative Joint Non-negative least squares Multi-Component MRF method (SPIJN-MRF) facilitates tissue parameter estimation for identified components as well as partial volume segmentations. The aim of this paper was to evaluate the accuracy and repeatability of the SPIJN-MRF parameter estimations and partial volume segmentations. This was done (1) through numerical simulations based on the BrainWeb phantoms and (2) using in vivo acquired MRF data from 5 subjects that were scanned on the same week-day for 8 consecutive weeks. The partial volume segmentations of the SPIJN-MRF method were compared to those obtained by two conventional methods: SPM12 and FSL. SPIJN-MRF showed higher accuracy in simulations in comparison to FSL- and SPM12-based segmentations: Fuzzy Tanimoto Coefficients (FTC) comparing these segmentations and Brainweb references were higher than 0.95 for SPIJN-MRF in all the tissues and between 0.6 and 0.7 for SPM12 and FSL in white and gray matter and between 0.5 and 0.6 in CSF. For the in vivo MRF data, the estimated relaxation times were in line with literature and minimal variation was observed. Furthermore, the coefficient of variation (CoV) for estimated tissue volumes with SPIJN-MRF were 10.5% for the myelin water, 6.0% for the white matter, 5.6% for the gray matter, 4.6% for the CSF and 1.1% for the total brain volume. CoVs for CSF and total brain volume measured on the scanned data for SPIJN-MRF were in line with those obtained with SPM12 and FSL. The CoVs for white and gray matter volumes were distinctively higher for SPIJN-MRF than those measured with SPM12 and FSL. In conclusion, the use of SPIJN-MRF provides accurate and precise tissue relaxation parameter estimations taking into account intrinsic partial volume effects. It facilitates obtaining tissue fraction maps of prevalent tissues including myelin water which can be relevant for evaluating diseases affecting the white matter.

On p-Brunn–Minkowski inequalities for intrinsic volumes, with 0le p

We prove the validity of the p-Brunn–Minkowski inequality for the intrinsic volume V_k, k=2,dots , n-1, of symmetric convex bodies in {{mathbb {R}}}^n, in a neighbourhood of the unit ball when one of the bodies is the unit ball, for 0le p<1. We also prove that this inequality does not hold true on the entire class of convex bodies of {{mathbb {R}}}^n, when p is sufficiently close to 0.

Multifunctional Self-Cross-Linked Copolymer Binder for High-Loading Silicon Anodes

Due to its ultra-high capacity and moderately low potential, silicon (Si) shows potential in replacing graphite-based anodes. Unfortunately, Si suffers from severe intrinsic volume expansions that restrict its practical use. Herein, we present a tailored copolymer, poly(acrylamide)-co-poly(hydroxymethylacrylate), p(AM-co-HMA), as a multifunctional binder for Si anodes, which forms a 3D network structure via a thermally induced self-cross-linking reaction. The formed cross-linked binder structure provides both covalent and hydrogen bonds and thereby improves both the adhesion between the individual electrode components and the current collector as well as the adhesion between the individual Si particles. Overall, the p(AM-co-HMA)-based binder offers superior electrochemical performance for high-loading Si anodes compared to traditionally applied binder systems.

Selective Gas Adsorption on Molecular Solids of a Hydrogen-bonding [3.3.3]Propellane

Abstract On a rigid three-dimensional π-framework, trinaphtho[3.3.3]propellane, hydrogen-bonding urea moieties were installed by successive functionalization with amino and carbonyl groups. The obtained perimidin-2-one-appended molecule gave void-containing solids without losing intrinsic free volume, being different from precursor molecules. The solids exhibited good adsorption selectivity for ethane, n-butane, and carbon dioxide over methane, because of the cavity surrounded by naphthalene rings and hydrogen-bonding perimidin-2-one units.

D-d hybridization controlled large-volume-change martensitic phase transition in Ni-Mn-Ti-based all-d-metal Heusler compounds

Martensitic phase transition in all-d-metal Heusler compounds was investigated by using first principles calculations. The large change in volume during martensitic phase transition and its physical origin were revealed in representative compound Ni2MnTi. It was found that the enhanced d-d interatomic hybridization due to intrinsic volume shrinkage during martensitic phase transition led to significant increase in thermodynamic driving force and great improvement in the deformation ability. Their strong correlations induced large volume change during martensitic phase transition. The tetragonal martensitic phase in Ni2MnTi preferred the weaker magnetic state. Herein, it was proposed that a metamagnetic martensitic phase transition from cubic ferromagnetic phase to tetragonal ferrimagnetic phase with large volume change can be realized by tuning d-d interatomic hybridization level. The investigations indicate that careful control of interatomic hybridization level in Ni-Mn-Ti-based compounds can serve as an inherent tuning parameter to design and explore high-performance candidates as phase transition materials for solid-state refrigeration.

Biocarbon-directed vertical δ-MnO2 nanoflakes for boosting lithium-ion diffusion kinetics

Manganese dioxide (MnO2) with high theoretical capacity (1230 mAh/g) and low cost is considered as a promising anode material for next generation high energy density lithium-ion (Li+) batteries. However, the intrinsic low electric conductivity and volume change during cycling process limit its applications. In this work, a unique δ-MnO2/C composite has been synthesized through the directed growth of 2D δ-MnO2 nanosheets on the cabbage-leaf-derived biocarbon. The biocarbon acts as both structure buffer to accommodate the volume expansion and conductive agent to promote electron and ion transport. Moreover, oriented δ-MnO2 nanosheets are beneficial for increasing contact area between electrode and electrolyte, thus providing more active sites and shortening the Li+ transmission routes. Electrochemical performances show that δ-MnO2/C displays large reversible capacity (754 mAh/g after 250 cycles at current density of 0.1 A/g), excellent rate capability as well as low charge transfer resistance (17.3 Ω), and high Li+ diffusion rate (DLi+ = 2.91 × 10-14 cm2/s) during the cycles. Furthermore, the density functional theory calculations reveal the lower Li+ migration barrier energies and improved Li+ diffusion kinetics in δ-MnO2/C hetero-layer. This study provides a novel strategy to design advanced nanocomposites, using natural plant-leaf derivatives as structure-directing agents, for the next generation energy storage and conversion systems.

Improving the measurement of intrinsic foot muscle morphology and composition from high-field (7T) magnetic resonance imaging

Magnetic resonance imaging (MRI) can be used to quantify intrinsic foot muscle morphology and composition. Due to the high spatial resolution required to adequately capture the architecturally complex anatomy, manual segmentation is time consuming and not clinically feasible. The aim of this study was to evaluate if a reduced number of MRI slices can be used to accurately estimate intrinsic foot muscle volume and composition. A three-dimensional 2-point Dixon sequence of the whole foot was acquired at 7-Tesla for thirteen asymptomatic individuals and twenty individuals with plantar heel pain. Slice intervals of 2, 3, 5, 10, 15 and 30 were used to calculate alternative muscle volume and composition, and were compared to reference values calculated from every available slice. Agreement between methods was assessed by calculating mean differences and 95% limits of agreement, and inspection of Bland –Altman plots. In both groups, slice intervals of 2, 3 and 5 provided excellent precision for all muscles (measurement error < 1%). Larger slice intervals of 10, 15 and 30 provided excellent precision for some muscles, but for other muscles (e.g. small forefoot muscles), error was up to 7.3%. Bland–Altman plots showed no systematic measurement bias. This study provides a quantitative basis for selecting a reduced number of slices to measure intrinsic foot muscle volume and composition from MRI. A slice interval of 10 may provide a balance between efficiency (36 mins vs. 6 h) and accuracy (error < 2.4%) across all intrinsic foot muscles in asymptomatic individuals and those with plantar heel pain.

Realizing highly reversible and deeply rechargeable Zn anode by porous zeolite layer

Aqueous zinc-ion batteries are of high interest due to their intrinsic safety, low cost, and high volume capacity. However, entrenched problems such as the dendrite growth and complex side reactions of zinc metal anodes severely reduce the reversibility of the battery. In this work, the modified porous natural zeolite materials are used to prepare a protective coating layer for the zinc anode. Such coating layer has a positive effect on inhibiting side reactions associated with dendrites as confirmed by test results. As a consequence, the modified zinc metal anodes can operate over 1200 h at 1 mA cm −2 with 0.5 mAh cm −2 in symmetric cells and achieve a lifespan up to 500 h at an ultrahigh areal capacity of 30 mAh cm−2 (10 mA cm−2 for 3 h). The full cells using modified Zn anodes and the V10O24-PANI nanosheet cathodes deliver a capacity of 332 mAh g−1 at 1 A g−1 and also show great cycling stability with 89% retained capacity after 1000 cycles at 10 A g−1. By solving the electrochemical problems of zinc anodes, the proposed strategy provides a new opportunity for the widespread applications of high-performance aqueous batteries in next-generation energy storage systems.

Interaction of the new inhibitor paxlovid (PF-07321332) and ivermectin with the monomer of the main protease SARS-CoV-2: A volumetric study based on molecular dynamics, elastic networks, classical thermodynamics and SPT

The COVID-19 pandemic has accelerated the study of drugs, most notably ivermectin and more recently Paxlovid (PF-07321332) which is in phase III clinical trials with experimental data showing covalent binding to the viral protease Mpro. Theoretical developments of catalytic site-directed docking support thermodynamically feasible non-covalent binding to Mpro. Here we show that Paxlovid binds non-covalently at regions other than the catalytic sites with energies stronger than reported and at the same binding site as the ivermectin B1a homologue, all through theoretical methodologies, including blind docking. We volumetrically characterize the non-covalent interaction of the ivermectin homologues (avermectins B1a and B1b) and Paxlovid with the mMpro monomer, through molecular dynamics and scaled particle theory (SPT). Using the fluctuation-dissipation theorem (FDT), we estimated the electric dipole moment fluctuations at the surface of each of complex involved in this study, with similar trends to that observed in the interaction volume. Using fluctuations of the intrinsic volume and the number of flexible fragments of proteins using anisotropic and Gaussian elastic networks (ANM+GNM) suggests the complexes with ivermectin are more dynamic and flexible than the unbound monomer. In contrast, the binding of Paxlovid to mMpro shows that the mMpro-PF complex is the least structurally dynamic of all the species measured in this investigation. The results support a differential molecular mechanism of the ivermectin and PF homologues in the mMpro monomer. Finally, the results showed that Paxlovid despite beingbound in different sites through covalent or non-covalent forms behaves similarly in terms of its structural flexibility and volumetric behaviour.

High-throughput finite-element design of dielectric composites for high-frequency copper clad laminates

Dielectric substrates with low dielectric constant and good thermal stability are highly desired for high-frequency and high-speed signal transmission. It is however challenging to rationally design the demand-satisfied polymer-based composites due to the inadequate understanding of the contradictory effect of inorganic fillers on modulating dielectric-thermal-mechanical properties. In this work, taking Polytetrafluoroethylene (PTFE)-SiO2 composite as the example, we perform high-throughput finite-element calculations to systematically study the filler effects on the dielectric constant of composites εrcomposite and the coefficient of thermal expansion of composites (CTE-c). A series of influencing factors including intrinsic property, volume fraction, shape, distribution, and orientation of fillers have been considered in our models to establish the structure-property mapping of dielectric composites. It is found that CTE-c is more sensitive to the filler structure of PTFE-SiO2 composites than εrcomposite. Finally, guided by the calculation results, a skeleton structure is proposed to realize the performance targets of εrcomposite< 2.3 and CTE-c < 60 ppm/K with lower SiO2 filler content. This work provides a universal data-driven strategy for the rational design of dielectric composites with multi-objective requirements, and it is expected to spark more experimental efforts to design novel dielectric composites for high-quality signal transmission.