Analytical Results Research Articles

The Volterra Integrable case. Novel analytical and numerical results

The Volterra Integrable case. Novel analytical and numerical results

Instabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise

Abstract We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.

Intrinsic anomalous, spin and valley Hall effects in ’ex-so-tic’ van-der-Waals structures

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) sandwiched between a semiconducting van-der-Waals material with strong spin-orbit coupling (e.g., WS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {WS}_2$$\\end{document}) and a ferromagnetic insulating vdW material (e.g. Cr2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Cr}_2$$\\end{document}Ge2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Ge}_2$$\\end{document}Te6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Te}_6$$\\end{document}). Due to the exchange proximity effect from one side and spin-orbit proximity effect from the other side of graphene, such a structure is referred to as graphene based ’ex-so-tic’ structure. First, we derive an effective Hamiltonian describing the low-energy states of the structure. Then, using the Green’s function formalism, we obtain analytical results for the Hall conductivities as a function of the Fermi energy and gate voltage. For specific values of these parameters, we find a quantized valley Hall conductivity.

Secure short-packet communications in power beacon-assisted IoT networks over Nakagami-m fading channels

In this work, we investigate short-packet communications in power beacon (PB)-assisted Internet-of-Things (IoT) networks, where an energy-constrained actuator first harvests energy from a dedicated PB, and then transmits confidential signals to a desired controller in the presence of an eavesdropper. We derive a closed-form lower bound approximation expression for the average achievable effective secrecy rate (AESR) over Nakagami-m fading channels. To gain more insights, we also present the asymptotic average AESR in the high signal-to-noise ratio (SNR) regime. Specifically, analytical results indicate that an average AESR floor appears with the increase of SNR. Moreover, a low complexity one-dimensional search method is employed to maximize the average AESR by optimizing the energy harvesting length. Monte-Carlo simulations are provided to corroborate our analysis.

Non-global logarithms up to four loops at finite-Nc for V/H+jet processes at hadron colliders

We extend our previous work [1] on calculating non-global logarithms in e+e− annihilation to Higgs/vector boson production in association with a single hard jet at hadron colliders. We analytically compute non-global coefficients in the jet mass distribution up to four loops using the anti-kt jet algorithm. Our calculations are performed in the eikonal approximation, assuming strong energy ordering for the emitted gluons, thus capturing only the leading logarithms of the distribution. We compare our analytical results with the all-orders large-Nc numerical solution. In general, the gross features of the non-global logarithm distribution observed in the e+e− case remain valid for the V/H+jet processes.

Two-state free-volume model for anomalous dynamics in supercooled water macromolecules undergoing liquid–liquid phase transition

Modelling anomalous dynamics of complex liquid water is a huge challenge due to its various condensed molecular structures and the associated liquid–liquid phase transitions (LLPTs). In this study, we considered, for the first time, the influences of free volume and entropy on LLPTs for both low-density liquid (LDL) and high-density liquid (HDL) waters. Firstly, we proposed a two-state free-volume model and combined with the Adam-Gibbs models to investigate the dynamic equilibria with free diffusion coefficient, viscosity, glass transition temperature and the anomalous dynamics in the two-state water. Free-energy equation was then developed to explore the constitutive relationships of free volume, entropy and anomalously dynamic behaviors. Finally, analytical results of the proposed two-state free-volume model were compared with the experimental data of two-state water reported in literature, and good agreements between them were demonstrated. This study offers a new physical insight into free volume for the anomalous dynamics and LLPTs in the two-state water.

Analysis of the underlying shield tunnel deformation caused by a newly built channel

As the development of underground space progresses, newly constructed waterways inevitably intersect with existing tunnels, posing significant challenges to the safety of underlying tunnels and making deformation control a critical issue in engineering design and construction. This study investigates the impact of waterway foundation pit excavation on the deformation of underlying tunnels. The research considers not only the vertical unloading at the bottom of the pit but also the horizontal unloading from the four side walls, which induces additional vertical stress fields in the underlying soil. These additional stresses are applied to the tunnel structure, modeled as a Pasternak elastic foundation beam, and the vertical tunnel deformation due to excavation unloading is calculated using the finite difference method. To validate the analytical results, a three-dimensional numerical model is employed. Furthermore, the study analyzes deformation trends under varying excavation sizes and the relative positions of the foundation pit and tunnel. The findings demonstrate that the proposed method provides a highly accurate, cost-effective, and efficient solution for predicting tunnel deformation during the excavation of small foundation pits. This research offers valuable insights for the design and assessment of underground structures in urban environments.

Lyapunov exponent as a signature of dissipative many-body quantum chaos

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large-q limit of a q-body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of q≥4 based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment. Published by the American Physical Society 2024

Sensitivity analysis for unmeasured confounding in estimating the difference in restricted mean survival time.

The difference in restricted mean survival time has been increasingly used as an alternative measure to the hazard ratio in survival analysis. Although some statistical methods have been developed for estimating the difference in restricted mean survival time adjusted for measured confounders in observational studies, the impact of unmeasured confounding on the estimate has rarely been assessed. We develop a novel sensitivity analysis for the estimate of the difference in restricted mean survival time with respect to unmeasured confounding. After formulating the sensitivity analysis problem as an optimization problem, we explain how to obtain the sensitivity range of the difference in restricted mean survival time efficiently and assess its uncertainty using the percentile bootstrap confidence interval. Analytic results are provided for some important survival settings. Simulation studies show that the proposed methods perform well in various settings. We illustrate the proposed sensitivity analysis method by analyzing data from the German Breast Cancer Study Group study.

Real-time Blood Pressure Prediction on Wearable Devices using Edge Based Deep Neural Networks: A Hardware-software Co-design Approach

This paper presents the hardware realization of a real-time blood pressure (BP) prediction model for wearable devices, utilizing long short-term memory (LSTM) deep neural networks (DNNs). The proposed system uses both electrocardiogram (ECG) and photoplethysmogram (PPG) signal values for BP prediction. It aims to address the limitations of traditional BP measurement methods, providing a low error, minimal computational overhead, more accurate and convenient alternative system for individuals with hypertension or at risk for cardiovascular diseases. The utilization of split matrix approach leads to a reduction in hardware complexity across the entire system. This technique involves breaking down the larger weight matrices used in the computations of DNNs into smaller matrices. This fragmentation results in a decrease in the complexity of the hardware responsible for performing matrix vector multiplications (MVMs) within LSTMs. The resultant architecture of the predictive model gains several advantages, including a lowered level of complexity in terms of the space occupied by individual cells, decreased processing delay, and reduced power consumption. Furthermore, this approach enables the achievement of a notably improved minimum achievable clock period of 2.972 ns. This prediction model can operate locally on wearable devices, reducing the reliance on cloud computing and improving privacy and security. The performance evaluations are carried out using both analytical and implementation results. The results indicate that the proposed model can be practically applied to real-world problems and can potentially enhance the accuracy of various machine-learning tasks.

A Review on Advancement in Analytical Quality by Design (AQbD)

Analytical Quality by Design (AQbD) represents a transformative methodology in pharmaceutical development, anchored in a systematic, risk-based, and data-driven framework. This approach optimizes analytical methods, fostering heightened product quality, efficient regulatory compliance, and informed decision-making. The industry's increasing acceptance of AQbD principles signifies a paradigm shift towards enhanced efficiency, sustainability, and global harmonization. This review comprehensively explores AQbD principles, regulatory perspectives, and its applications, particularly in analytical method development, including high-performance liquid chromatography (HPLC) and high-performance thin-layer chromatography (HPTLC). Emphasis is placed on the symbiotic relationship between AQbD and analytical method validation (AMV), elucidating their collective role in ensuring reliable and accurate analytical results. Integrating AQbD in method transfer, automation, and control strategies underscores its pivotal role in achieving robust, efficient, and compliant analytical processes. The review delves into lifecycle management and continuous improvement, coupled with AQbD principles, ensuring sustained method reliability throughout the pharmaceutical product lifecycle. AQbD's significant contribution to pharmaceutical lifecycle management, optimization, and change control is explored, emphasizing its systematic, data-driven, and risk-based approach to method development, validation, and ongoing enhancement. This review illuminates AQbD's transformative impact on pharmaceutical analysis, aligning with industry trends toward quality, efficiency, and regulatory compliance.

A Simple Method to Evaluate the Bearing Capacity of Concrete-Filled Steel Tubes with Rectangular and Circular Sections: Beams, Columns, and Beam–Columns

This study investigates the behavior and capacity of concrete-filled steel tubes (CFTs) with rectangular and circular sections under various loading conditions: axial loads, pure-bending, and combined axial load-bending moments. A finite element-based numerical model is developed and validated against existing experimental data. Using an extensive databank generated from finite element analysis, this research proposes analytical empirical relations for determining the bearing capacity of rectangular and circular composite beams, columns, and beam–columns. These relations provide a direct, concise, and efficient method for calculating the ultimate strength of CFT members, making them valuable for engineering design. Comparisons between the proposed analytical results and previous experimental studies demonstrate the high accuracy of this method in analyzing rectangular and circular CFT member behavior. The findings contribute to a better understanding of CFT structural performance and offer practical tools for designers working with these composite elements.

The determination of bisphenols contained in food-related products with increased accuracy provided by the H-point Standard Addition Method (HPSAM)-based methodology

The basic version of the H-point standard addition method and its variants have been developed with an increased number of measurement conditions (from two to five conditions allowed for differentiation of sensitivity). The methodology adapted to the signal increment and generalized versions was used for the determination of the harmful compounds from the group of bisphenols (bisphenol A, S, and F) using high-performance liquid chromatography with a diode array detector. This approach in theoretical and experimental studies allowed for obtaining high-quality results after eliminating all types of interference effects: multiplicative, additive, and nonlinear. The analysis of food-related samples, such as store receipts and canned food, confirmed the effectiveness of the developed methodology. The analytical results were distinguished by very good accuracy (RE<5 %, RV∼100 %) and precision (CV≤4 %). The approach can be successfully applied to various analytical systems (RGB model) and is characterized by a high greenness value (AGREE approach).

Production of double P-wave heavy quarkonia at a super Z factory

The production of double P-wave heavy quarkonia is studied systematically within the framework of non-relativistic quantum chromodynamics at the exclusive process of the electron–positron collision annihilation at the CM energy s=91.1876\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=91.1876$$\\end{document} GeV of the Z0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z^0$$\\end{document} pole, i.e., double P-wave charmonia, double P-wave Bc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c$$\\end{document} mesons, and double P-wave bottomonia in e+e-→γ∗/Z0→|(QQ′¯)[n]⟩+|(Q′Q¯)[n′]⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-\\rightarrow \\gamma ^*/Z^0 \\rightarrow |(Q\\bar{Q'})[n]\\rangle +|(Q'\\bar{Q})[n^\\prime ]\\rangle $$\\end{document} (Q/Q′=c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q/Q'=c$$\\end{document}- or b-quarks) at a future super Z factory, where [n] or [n′]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[n^\\prime ]$$\\end{document} stands for the color-singlet [1P1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^1P_1]$$\\end{document} and [3PJ]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^3P_J]$$\\end{document} (J=0,1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J=0,1,2$$\\end{document}) Fock states. As an improved trace technology is useful for calculating the complicated double P-wave channels, the analytical result can be obtained at the amplitude level. According to our study, the generation rates for the double P-wave heavy quarkonia at the future super Z factory are considerable. The values obtained for the total cross sections of the double P-wave charmonium for σ(|(cc¯)[1]⟩+|(cc¯)[1]⟩)=4.191-0.498+0.489×10-3fb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma {(|(c\\bar{c})[1]\\rangle +|(c\\bar{c})[1]\\rangle )}=4.191^{+0.489}_{-0.498}\ imes 10^{-3}~fb$$\\end{document}, the total cross sections of the double P-wave Bc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c$$\\end{document} mesons for σ(|(cb¯)[1]⟩+|(bc¯)[1]⟩)=0.2045-0.0080+0.0084fb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma {(|(c\\bar{b})[1]\\rangle +|(b\\bar{c})[1]\\rangle )}=0.2045^{+0.0084}_{-0.0080}~fb$$\\end{document}, and the total cross sections of the double P-wave bottomonium for σ(|(bb¯)[1]⟩+|(bb¯)[1]⟩)=5.244-0.136+0.134×10-3fb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma {(|(b\\bar{b})[1]\\rangle +|(b\\bar{b})[1]\\rangle )}=5.244^{+0.134}_{-0.136}\ imes 10^{-3}~fb$$\\end{document}. The main uncertainties come from the mass of heavy quarkonia and the corresponding first-derivative radial wave functions at the origin under the Buchmüller–Tye (BT) potential. The number of events in the production of double P-wave charmonium, Bc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c$$\\end{document}-meson, and bottomonium states via e-e+→γ∗/Z0→|(QQ¯′)[n]⟩+|(Q′Q¯)[n′]⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^-e^+\\rightarrow \\gamma ^*/Z^0 \\rightarrow |(Q\\bar{Q}')[n]\\rangle + |(Q'\\bar{Q})[n^\\prime ]\\rangle $$\\end{document} at the integrated luminosity L≈1034cm-2s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{L}\\approx 10^{34}cm^{-2}s^{-1}$$\\end{document} at the super Z factory is almost unobservable.

Household demand for community- and rooftop-solar electricity: conceptual and numerical assessments

ABSTRACT This paper characterizes the trade-offs faced by households in deciding how much solar power to produce privately on their rooftops or to subscribe to in a community solar project (or, ‘green electricity plan’), and how these trade-offs are influenced by a regulator's pricing scheme. We characterize a model where representative households choose their rooftop and community-solar consumption levels and respond to the regulator's scheme. Within the model's conceptual and numerical frameworks, we derive a suite of household comparative static effects and explore four key implications pertinent to the growth of rooftop and community solar within a given community: (1) the extent to which the regulator must adjust its pricing scheme to achieve a community-wide solar electricity standard, (2) the potential of a ‘death spiral’ experienced by the regulator, (3) the effect of a ‘solar tax’ levied by the regulator on the production of solar electricity by rooftop-solar households, and (4) adoption of ‘behind-the-meter’ battery storage by rooftop-solar households. We obtain both analytical and numerical results for each of these implications, enabling us to better understand the underlying conditions governing a representative household's responses to incentives provided by a regulator, and the social implications of these responses.

Stability Analysis of the Transmission Model of TB-HIV Co-Dynamics with Vaccination and Treatment

This study aims to analyse and determine the stability of the equilibrium point of the spread model consists of TB infection, HIV infection, and TB-HIV co-infection disease. This model considers eight compartments, namely unvaccinated susceptible, vaccinated susceptible, exposed, infected with TB, infected with HIV, infected with TB and HIV, treatment, and recovered by considering vaccination and treatment in the compartments as the strategies to manage spread of the diseases. The stability of non-endemic equilibrium point is carried out by determining the basic reproduction number and eigenvalues. Simulation is conducted to investigate effect of vaccination and treatment. By giving appropriate values of parameters and varying values of vaccination rate we found that increasing value of vaccination rate will reduce and eliminate TB infection, HIV infection, and TB-HIV co-infection disease from the population. The curve solutions of the dynamics of each compartment are given to confirm the analytical results.

4D-printed shape-programmable [H+]-responsive needles for determination of urea

Four-dimensional printing (4DP) technologies are revolutionizing the fabrication, functionality, and applicability of stimuli-responsive analytical devices. More practically, 4DP technologies are effective in fabricating devices with complex geometric designs and functions, and the degree of shape programming of 4D-printed stimuli-responsive devices can be optimized to become a reliable analytical strategy. Although shape-programming modes play a critical role in determining the analytical characteristics of 4D-printed stimuli-responsive sensing devices, the effect of shape-programming modes on the analytical performance of 4D-printed stimuli-responsive devices remains an unexplored subject. We employed digital light processing three-dimensional printing (3DP) with acrylate-based photocurable resins and 2-carboxyethyl acrylate (CEA)-incorporated photocurable resins for 4DP of the bending, helixing, and twisting needles. Upon immersion in samples with pH values above the pKa of CEA, the electrostatic repulsion among the dissociated carboxyl groups of polyCEA caused swelling of the CEA-incorporated part and [H+]-dependent shape programming. When coupling with the derivatization reaction of the urease-mediated hydrolysis of urea, the decline in [H+] induced shape programming of the needles, offering reliable determination of urea based on the shape-programming angles. After optimizing the experimental conditions, the helixing needles provided the best analytical performance, with the method's detection limit of 0.9 μM. The reliability of this analytical method was validated by determining urea in samples of human urine and sweat, fetal bovine serum, and rat plasma with spike analyses and comparing these results with those obtained from a commercial assay kit. Our demonstration and analytical results suggest the importance of optimizing the shape-programming modes to improve the analytical performance of 4D-printed stimuli-responsive shape-programming sensing devices and emphasize the benefits and applicability of 4DP technologies in advancing the development and fabrication of stimuli-responsive sensing devices for chemical sensing and quantitative chemical analyses.

Exact results of the one-dimensional repulsive Hubbard model

We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and thek-Λstring bound states at arbitrary driving fields, showing subtle differences in spin magnons and chargeη-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.

Trends and topics: Characterizing echo chambers’ topological stability and in-group attitudes

Nowadays, online debates focusing on a wide spectrum of topics are often characterized by clashes of polarized communities, each fiercely supporting a specific stance. Such debates are sometimes fueled by the presence of echo chambers, insulated systems whose users’ opinions are exacerbated due to the effect of repetition and by the active exclusion of opposite views. This paper offers a framework to explore how echo chambers evolve through time, considering their users’ interaction patterns and the content/attitude they convey while addressing specific controversial issues. The framework is then tested on three Reddit case studies focused on sociopolitical issues (gun control, American politics, and minority discrimination) during the first two years and a half of Donald Trump’s presidency and on an X/Twitter dataset involving BLM discussion tied to the EURO 2020 football championship. Analytical results unveil that polarized users will likely keep their affiliation to echo chambers in time. Moreover, we observed that the attitudes conveyed by Reddit users who joined risky epistemic enclaves are characterized by a slight inclination toward a more negative or neutral attitude when discussing particularly sensitive issues (e.g., fascism, school shootings, or police violence) while X/Twitter ones often tend to express more positive feelings w.r.t. those involved into less polarized communities.

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.