Expansion Properties Research Articles

AMITE: A Novel Polynomial Expansion for Analyzing Neural Network Nonlinearities.

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor and Chebyshev methods, asymptotics, and many numerical approaches. We find that, while these have useful properties individually, such as exact error formulas, adjustable domain, and robustness to undefined derivatives, there are no approaches that provide a consistent method, yielding an expansion with all these properties. To address this, we develop an analytically modified integral transform expansion (AMITE), a novel expansion via integral transforms modified using derived criteria for convergence. We show the general expansion and then demonstrate an application for two popular activation functions: hyperbolic tangent and rectified linear units. Compared with existing expansions (i.e., Chebyshev, Taylor, and numerical) employed to this end, AMITE is the first to provide six previously mutually exclusive desired expansion properties, such as exact formulas for the coefficients and exact expansion errors. We demonstrate the effectiveness of AMITE in two case studies. First, a multivariate polynomial form is efficiently extracted from a single hidden layer black-box multilayer perceptron (MLP) to facilitate equivalence testing from noisy stimulus-response pairs. Second, a variety of feedforward neural network (FFNN) architectures having between three and seven layers are range bounded using Taylor models improved by the AMITE polynomials and error formulas. AMITE presents a new dimension of expansion methods suitable for the analysis/approximation of nonlinearities in neural networks, opening new directions and opportunities for the theoretical analysis and systematic testing of neural networks.

Sintering Temperature Effect of Near-Zero Thermal Expansion Mn3Zn0.8Sn0.2N/Ti Composites.

Metal matrix composites with near-zero thermal expansion (NZTE) have gained significant popularity in high-precision industries due to their excellent thermal stability and mechanical properties. The incorporation of Mn3Zn0.8Sn0.2N, which possesses outstanding negative thermal expansion properties, effectively suppressed the thermal expansion of titanium. Highly dense Mn3Zn0.8Sn0.2N/Ti composites were obtained by adjusting the fabrication temperature. Both composites fabricated at 650 °C and 700 °C exhibited NZTE. Furthermore, finite element analysis was employed to investigate the effects of thermal stress within the composites on their thermal expansion performance.

Pressure-induced elastic softening and negative thermal expansion in the antiperovskite-type MFe3N (M=Fe, Ni, Pd, and Pt) compounds

Based on the first-principles calculations, the effects of pressure on the structural, magnetic, lattice dynamical, elastic and thermal expansion properties of TMFe3N (TM = Ni, Pd, Pt) compound are studied, and a comparison with the parent phase Fe4N is performed. The calculated total enthalpy reproduces that the Ni, Pd and Pt atoms favor staying in the Fe 1a site of parent phase, and forming the ferromagnetic state. The substitution of Ni, Pd and Pt atoms reduces the critical pressure of ferromagnetic collapse of the parent phase, while enhancing its dynamic stability when subjected to high pressure. The results of the elastic constants indicate that substituting Ni, Pd and Pt atoms can improve the mechanical characteristics of the parent phase. Pressure-induced elastic softening and negative thermal expansion are found in both Fe4N and TMFe3N (TM = Ni, Pd, Pt) compounds. These two abnormal behaviors are analyzed with the magnetoelastic force and the competition among the spontaneous volume magnetostriction effect, pressure-induced effect, and thermal effect within the system, respectively.

Building Negative-Thermal-Expansion Protective Layers on the Grain Boundary of Ni-rich Cathodes Enables Safe and Durable High Voltage Lithium-Ion Batteries.

Ni-rich layered oxide cathode materials demonstrate high energy densities for Li-ion batteries, but the electrochemically driven thermal runaway and mechanical degradation remain their long-standing challenges in practical applications. Herein, it presents a novel ZrV2 O7 (ZVO) coating with negative thermal expansion properties along the secondary particles and primary particle grain boundaries (GBs), to simultaneously enhance the structural and thermal stability of LiNi0.8 Co0.1 Mn0.1 O2 (NCM811). It unveils that, such an architecture can significantly enhance the electronic conductivity, suppress the microcracks of GBs, alleviate the layered to spinel/rock-salt phase transformation, and meanwhile relieve the lattice oxygen loss by increasing the oxygen vacancy formation energy increased (1.43 vs 1.90eV). Consequently, the ZVO-coatedNCM811 material demonstrates a remarkable cyclability with 86.5% capacity retention after 100 cycles, and an outstanding rate performance of 30C under a high-voltage of 4.6V, outperforming the state-of-the-art literature. More importantly, the Li+ transportation can be readily blocked at 120°C by the negative-thermal-expansion ZVO coating, thus avoiding the high-temperature thermal runaway.

Novel metamaterial structures with negative thermal expansion and tunable mechanical properties

The thermal expansion and stiffness characteristics are significant in determining the responses of lightweight mechanical metamaterials in a thermal environment. This paper proposed a novel trapezoid unit with negative thermal expansion (NTE) by three conventional materials with positive thermal expansion, and constructed a series of lightweight metamaterials by sharing edges and sharing vertexes. The effective linear coefficients of thermal expansion (CTE) of these metamaterial structures are theoretically explored by considering axial and bending deformations. Based on Euler beam theory, the effective linear elastic stiffnesses of these metamaterials are given accurately by the stiffness matrix method. The accuracy of the theoretical effective CTE and stiffness is well verified by numerical modeling. The effective linear CTE, elastic stiffness, and Poisson's ratio of these metamaterials can be programmable by controlling geometrical parameters and material properties. The NTE effect can be achieved in ET, EQ, EH, and VT metamaterials due to the presence of re-entrant structures, in which the ET metamaterial can fulfill the maximum magnitude NTE. The NTE and negative Poisson's ratio can simultaneously be realized in EQ metamaterial. Significantly, a broader range of CTE from negative to positive values can be fulfilled in these metamaterials compared with the conventional triangle unit. Furthermore, the high specific stiffness with extremely low thermal stress can be obtained in EQ, VT, and VH metamaterials, which benefits the stability controlling and enhancing natural frequencies of structures in a thermal environment.

Study on the mechanical properties of self-compacting recycled aggregate concrete using CFB slag as fine aggregate

To reveal the influence of CFB slag on the mechanical and expansion properties of self-compacting recycled aggregate concrete (SCRAC), five SCRACs with different CFB slag replacement amounts were made, the cubic compressive strength test, the splitting tensile strength test, the axial compressive strength test, and the dry shrinkage test were carried out. The failure processes and failure forms of SCRAC under compression and tension were observed. The effects of the influence of the CFB slag replacement rate on the basic mechanical properties of SCRAC were analyzed. The conversion relationship between various mechanical indicators of SCRACs was explored. The drying shrinkage performance of SCRAC was tested using the grey theory. The test results indicate that the compressive failure of SCRAC using CFB slag as fine aggregate is similar to that of SCC. The results show that the cubic compressive strength, splitting tensile strength, and axial compressive strength of self-compacting recycled concrete are the highest when the sand replacement ratio of CFB slag is 10%. The proposed conversion relationship between the cubic compressive strength of SCRAC and other mechanical properties indexes has high accuracy. GM (1, N) model and grey correlation analysis were established to analyze the influencing factors of drying shrinkage of SCRAC. The drying shrinkage deformation of SCRAC using CFB slag as fine aggregate has a hyperbola relationship with time, and a lower CFB slag sand replacement rate can compensate for the shrinkage of SCRAC.

A quasi-ergodic approach to non-integer base expansions

P. Erdős et al. proved in 1990 that every nontrivial number has a continuum of expansions on two-letter alphabets in every base smaller than the Golden ratio, and that this property fails for the Golden ratio base. It was shown in a recent paper of Baiocchi et al. that if we replace the powers of the Golden ratio by the closely related Fibonacci sequence, then the resulting integer base expansions still have the continuum expansion property. The proof heavily relied on the special properties of the Golden ratio. The difficulty came from the fact that the new expansions do not have any more the ergodic structure of non-integer base expansions. In this paper we introduce a new “quasi-ergodic” approach that allows us to handle many more general cases. We apply this approach to Baker's generalized Golden ratios.

A new approach to improving the water resistance of MOC-solidified sludge using [formula omitted] ions

With the growing sustainability concerns and awareness of environmental conservation, utilizing magnesium-based cement in construction has garnered considerable attention in recent years. In this work, a novel and sustainable approach to treating sludge has been developed by incorporating NaHCO3 to enhance the properties of MOC (Magnesium Oxychloride Cement)-solidified sludge. Different properties were determined through various experimental techniques, such as unconfined compressive strength (UCS), durability, scanning electron microscopy (SEM), X-ray diffraction (XRD) tests, and mercury intrusion porosimetry (MIP) to assess the impact of NaHCO3 content, curing age, and other factors on the strength, water resistance, microstructure, and reaction products of MOC-solidified sludge. The results indicate that adding NaHCO3 significantly enhanced the compressive strength and water resistance of MOC-solidified sludge, with an optimum NaHCO3 content of 50%. However, excessive NaHCO3 content led to a reduced MOC content, as evidenced by a strength loss rate of approximately 50% when NaHCO3 content reached 200%. Adding NaHCO3 also produces hydrated magnesium carbonates in solidified sludge in addition to Phase 5 and Brucite (Mg(OH)2). The expansion and cementation properties of these reaction products effectively filled the pores of the samples, facilitating the bonding of soil particles, establishing a stable spatial network structure, and improving the resulting strength of MOC-solidified sludge.

Development of a Multiscale Mechanistic Modelling Framework Integrating Differential Cellular Kinetics of CAR-T Cell Subsets and Immunophenotypes in Cancer Patients.

Chimeric antigen receptor (CAR) T-cell subsets and immunophenotypic composition of the pre-infusion product, as well as their longitudinal changes following infusion, are expected to affect CAR-T cell expansion, persistence, and clinical outcomes. Herein, we sequentially evolved our previously described cellular kinetic-pharmacodynamic (CK-PD) model to incorporate CAR-T cell product-associated attributes by utilizing published preclinical and clinical datasets from two affinity variants (FMC63 and CAT19 scFv) anti-CD19 CAR-T cells. In step 1, a unified cell-level PD model was used to simultaneously characterize the in vitro killing datasets of two CAR-Ts against CD19+ cell lines at varying effector: target (E: T) ratios. In step 2, an augmented CK-PD model for anti-CD19 CAR-Ts was developed, by integrating CK dataset(s) from two bioanalytical measurements (qPCR and flow cytometry) in cancer patients. The model described the differential in vivo expansion properties of CAR-T cell subsets. The estimated expansion rate constant was ~1.12-fold higher for CAR+CD8+ cells in comparison to CAR+CD4+ T cells. In step 3, the model was extended to characterize the disposition of four Immunophenotypic populations of CAR-T cells, including stem-cell memory (TSCM ), central memory (TCM ), effector memory (TEM ) and effector (TEFF ) cells. The model adequately characterized the longitudinal changes in immunophenotypes post anti-CD19 CAR-T cell infusion in acute lymphocytic leukemia paediatric patients. Polyclonality in the pre-infusion product was identified as a categorical covariate influencing differentiation of immunophenotypes. In the future, this model could be leveraged a priori towards optimizing the composition of CAR-T cell infusion product, and further understand the CK-PD relationship in patients.

Effects of MEA Type and Curing Temperature on the Autogenous Deformation, Mechanical Properties, and Microstructure of Cement-Based Materials.

MgO expansive agent (MEA) has the potential to meet the shrinkage compensation demands for concrete in different types of structures due to its designable reactivity and expansion properties. This study investigated the impact of three types of MEAs with different reactivities as well as curing temperature on the autogenous deformation, mechanical properties, and the microstructure of cement-based materials. The results showed that MEA type R exhibits a faster and larger hydration degree and expansion in cement mortars than MEA type M or type S in early ages under 20 °C, while when the curing temperature increases to 40 °C and 60 °C, MEA type M and type S present with significant accelerations in the hydration degree, leading to accelerated expansion rates and significantly increased expansion values compared to MEA type R. Under 40 °C, 5% MEA type M and type S present with 2.2 times and 1.1 times higher expansion in mortars than 5% MEA type R, respectively, and 8% MEA type M and type S present with 7.1 times and 5.6 times higher expansion in mortars than 8% MEA type R, respectively. Under 60 °C, 5% MEA type M and type S present 4.0 times and 3.1 times higher expansion in mortars than 5% MEA type R, respectively, and 8% MEA type M and type S present 7.0 times and 6.6 times higher expansion in mortars than 8% MEA type R, respectively. However, the increase in porosity, especially for large pores with pore size greater than 50 nm as well as the microcracks induced by the 8% dosage of MEA type M, type S, and high curing temperature of 60 °C, result in a decrease in strength of about 30% for the cement mortars. The results indicate that MEA type R is more suitable for shrinkage compensation of cement-based materials with lower temperatures, while MEA type M and type S are more suitable for shrinkage compensation of cement-based materials with higher temperatures. Under high-temperature and low-constraint conditions, the dosage of MEA needs to be strictly controlled to prevent negative effects on the microstructure and strength of cement-based materials.

Enable Multi-Stimuli-Responsive Biomimetic Actuation with Asymmetric Design of Graphene-Conjugated Conductive Polymer Gradient Film.

In this paper, multiresponsive actuators based on asymmetric design of graphene-conjugated poly(3,4-ethylene dioxythiophene): poly(styrenesulfonate) (PEDOT:PSS) gradient films have been developed by a simple drop casting method. The biomimetic actuation is attributed to the hygroscopic expansion property of PEDOT:PSS and the gradient distribution of graphene sheets within the film, which resembles the hierarchical swelling tissues of some plants in nature. Graphene-conjugated PEDOT:PSS (GCP) actuators exhibit reversible bending behavior under multistimuli such as moisture, organic vapor, electrothermal, and photothermal heating. Noticeably, the bending curvature reaches 2.15 cm-1 under applied voltage as low as 1.5 V owing to the high electrical conductivity of GCP actuator. To mimic the motions of nyctinastic plants, a GCP artificial flower that spreads its petals under sunlight illumination has been fabricated. GCP actuators have been also demonstrated as intelligent light-controlled switches for light-emitting diodes and smart curtains for thermal management. Not only do the GCP gradient films exhibit potential applications in flexible electronics and energy harvesting/storage devices but also the facile fabrication of multiresponsive GCP actuators may shed light on the development of soft robotics, artificial muscles, wearable electronics, and smart sensors.

Magnetic properties of the FCC and BCC phases of (MnFeCoNi)80Cu[formula omitted] ([formula omitted]: Al, Ga) high-entropy alloys

In this work, the FCC-BCC phase transition in (MnFeCoNi)80Cu20−xZx (Z: Al, Ga) high entropy alloys were investigated on the basis of structural, magnetic, hardness and thermal expansion properties. It is found that the equiatomic MnFeCoNiCu alloy is FCC and exhibits mixed ferromagnetic/anti-ferromagnetic interactions with a Curie temperature, Tc, close to room temperature. However, the BCC structure emerges with increasing amount of Al (10 at%) and Ga (15 at%) with additional ferromagnetic interactions and associated Tcs. It is evidenced that in terms of the valence electron concentration and the average magnetic moment values, the investigated HEAs obey the Slater-Pauling rule in a region close to the Heusler alloys. Additionally, they may exhibit similar physical properties like Invar property with low thermal expansion coefficient with the 3d-transition metal-alloys having same valence electron concentration.

Manipulating non-collinear antiferromagnetic order and thermal expansion behaviors in triangular lattice Mn3Ag1−xSn(Ge)xN

Magnetic materials with non-collinear spin orderings provide an outstanding platform to probe spintronic phenomena owing to their strong spin-orbit coupling (SOC) and unique Berry phase. It is thus important to obtain a non-collinear antiferromagnetic (AFM) phase at room temperature (RT). Significantly, the discovery of novel materials with nearly zero thermal expansion (ZTE) property near RT is required and pursued for avoiding thermal stress and fracture in spintronic devices. Herein, the doping of Sn (Ge) at the Ag site in the triangular lattice Mn3Ag1−xSn(Ge)xN compounds increases effectively the Néel point and makes the interesting non-collinear Γ5g AFM phase exist above RT. The magnetic phase diagrams with Γ5g phase up to 498 K were built by the combined analysis of neutron powder diffraction (NPD), magnetic measurements, electronic transport, and differential scanning calorimetry (DSC). The thermal expansion behaviors of Mn3Ag1−xSn(Ge)xN were modulated, and the nearly ZTE above RT was achieved in Mn3Ag0.5Ge0.5N within Γ5g AFM ordering. Our findings offer an effective way to tailor the non-collinear AFM ordering and correlated thermal expansion behavior for potential use in the emerging field of thermal stress-free magnetic chip materials.

Thermal expansion and mechanical properties of urethane-modified epoxy bonded CFRP/steel joints at low and high temperatures for automotive

Long-term reliability is critical in automobiles owing to their frequent exposure to the external environment and lengthy operational durations. Using dissimilar materials as adhesives to reduce the weight of vehicles results in a mismatch of coefficients of thermal expansion (CTE). Difference in CTE causes constant internal stress at the adhesive interface when the temperature changes, leading to delamination of the adhesive at the interfaces, microcrack initiations, and crack propagations. Therefore, a blend of linear urethane prepolymer and epoxy was tested to alleviate stress concentration. Dynamic mechanical analysis (DMA) was performed to determine the modulus according to the urethane content, while tensile strength was measured to evaluate changes in the physical properties. It was observed that increasing the urethane content decreased the modulus but progressively enhanced the tensile strength elongation rate. The lap shear strength specimen was thermally shocked to validate the decrease relative to the initial value based on the cycles. Consequently, combining urethane and epoxy successfully enhanced the elongation and reduced the internal stress caused by temperature changes.

Dynamical properties of convex cocompact actions in projective space

AbstractWe give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups that are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.

Einstein beams and the diffractive aspect of gravitationally-lensed light

The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light interferes, but observing this diffractive aspect of gravitational lensing has not been possible due to coherency challenges caused by the finite size of the sources or lack of near-perfect alignment. In this article, we report on the observation of these wave effects of gravitational lensing by recreating the lensing conditions in the laboratory via electro-optic deflection of coherent laser light. The lensed light produces a beam containing regularities, caustics, and chromatic modulations of intensity that depend on the symmetry and structure of the lensing object. We were also able to observe previous and new geometric-optical lensing situations that can be compared to astrophysical observations. This platform could be a useful tool for testing numerical/analytical simulations, and for performing analog simulations of lensing situations when they are difficult to obtain otherwise. We found that laboratory lensed beams constitute a new class of beams, with long-range, low expansion, and self-healing properties, opening new possibilities for non-astrophysical applications.

Synthesis and thermal expansion property of Cr2W3O12 doped with WO3

Cr2W3O12, one of the members of the negative thermal expansion family of A2M3O12, is reported to be prepared by the solid-state method with Cr2O3 and WO3, which was impossible before. Here, the synthesis of Cr2W3O12 is carried out by solid-state sintering. The powder mixture of Cr2O3 and WO3 is obtained using Zn(CH3COO)2 · 2H2O as the catalyst. When Zn(CH3COO)2 · 2H2O (0–25 mol. %) is added to the mixture of Cr2O3 and WO3 with 15 and 20 mol. % of excess WO3, much of the Cr2W3O12 is formed especially because of the addition of 10 and 15 mol. % of Zn(CH3COO)2 · 2H2O. For comparison, commercial ZnO is used as an addition, but its catalytic role is much lower than that of Zn(CH3COO)2 · 2H2O. The roles of addition of Zn(CH3COO)2 · 2H2O and excess WO3 are ascribed to compensate the volatility of WO3 and speed up the reaction of Cr2O3 + 3WO3 → Cr2W3O12 by the catalytic action of Zn(CH3COO)2 · 2H2O, respectively. The prepared Cr2W3O12 samples show positive thermal expansion due to the influence of excess WO3.

Effect of quartz grain size on elastic and thermal expansion properties of porcelain

Effect of quartz grain size on elastic and thermal expansion properties of porcelain

A cobalt(II) hydrogen-bonded organic framework exhibiting uniaxial negative thermal expansion and field-induced slow magnetic relaxation

The magnetic and thermal expansion properties of a cobalt(II) hydrogen-bonded organic framework (CoHOF), [Co(H2O)6](NPS)2 (1, HNPS = naphthalene-2-sulphonic acid), constructed by hexaaquacobalt(II) and organsulfonate were reported. Single-crystal X-ray diffraction reveals a porous 2D hydrogen-bonded framework of 1 sustained by multiple and charge-assisted intermolecular hydrogen bonding interactions. Variable-temperature single-crystal combined with powder X-ray diffraction and thermal gravimetric analyses confirms the high thermal stability of the CoHOF. The dynamic changes of the crystal lattice indicate uniaxial negative thermal expansion (NTE) behavior along the c-axis direction through a possible slippage motion. Magnetic measurements indicate the Co2+ ions show uniaxial magnetic anisotropy with D = −92.5 cm−1. A.C. susceptibility measurements reveal field-driven slow magnetic relaxation of 1. These results provide a rare cobalt(II) hydrogen-bonded organic framework showing single-ion magnetism and negative thermal expansion properties.

Macroscopic negative differential thermal resistance in the overlapping graphene homojunction structure

As one of the most potential ways to manipulate heat, thermal functional devices have achieved several breakthroughs in recent years, but are still limited to theoretical simulations. One of its theoretical bases is the existence of the negative differential thermal resistance (NDTR). However, most of the existing systems where the phenomenon of NDTR is found are atomic-level systems. In order to realize the macroscopic NDTR and provide effective theoretical guidance and support for the practical realization of thermal functional devices, we construct the overlapping graphene homojunction model, using the negative thermal expansion property of graphene to modify the overlapping area, and thus regulating the heat flow. The COMSOL-MATLAB co-simulation is used to perform calculations through negative feedback loops. It is found that the NDTR phenomenon exists under certain parameter conditions, which can provide new ideas and bring more opportunities for the experimental realization of nonlinear thermal functional devices.