Mathematical Conditions Research Articles

Assessment of Free Energy Functions for Sand

ABSTRACTThe advantages of constitutive models in energy‐conservation frameworks have been widely addressed in the literature. A key component is choosing an appropriate energy potential to derive the hyperelastic constitutive equations. This article investigates the advantages and limitations of different energy potentials found in the literature based on mathematical conditions to guarantee numerical stability, such as the desired order of homogeneity, positive and non‐singular stiffness within the application range, and equivalent Poisson's ratio from a constitutive modelling standpoint. Potentials meeting the aforementioned criteria are employed to simulate the response envelopes of Karlsruhe fine sand (KFS). Moreover, the performance of the potentials, in conjunction with plasticity theories, is examined. To achieve this, the hyperelastic constitutive equations have been coupled with the bounding surface plasticity model of Dafalias and Manzari to reproduce the soil response in a hyperelastic–plastic frame. Finally, one of the potentials is modified, whereas recommendations for incorporating other appropriate free energy functions into different soil constitutive models are presented. Furthermore, 100 closed elastic strain cycles have been simulated with the bounding surface plasticity model of Dafalias and Manzari considering the original hypoelastic stiffness and hyperelastic–plastic constitutive equations. Using the hypoelastic framework in the simulation led to stress accumulation after 100 closed elastic strain loops, while a reversible response was predicted using the hyperelastic stiffness tensor.

Implementation of Software for Learning Message Transmission Using Morse Code

The article presents the implementation of software for training message transmission using Morse code. This is a method of sign coding when letters of the alphabet, numbers, punctuation marks and other symbols are represented as sequences of short and long signals called dots and dashes. It is intended for transmission over serial communication channels. A unique feature of Morse code is the ability to be encoded and decoded by humans without the use of special terminal devices. The paper shows a software implementation of processing input characters using a telegraphic key, it includes: various mathematical requirements and conditions that allow you adjusting to each user, provided that his input speed will either fall or remain unchanged. However, it is possible to adjust the minimum duration threshold in such a way that the system will slowly adapt to a slow increase in input speed. At the same time, the higher the value of the minimum threshold, the faster the adaptation is; however, it will fall within the limit of the maximum input speed that the device can recognize. During the implementation of the program, a flow chart of message transliteration, signal reception and transmission was developed. The whole program implements the following functions: a simple and intuitive translator, with audio output, a simulator for consolidating the skill of entering Morse code using a key; consolidating the skills of recognition and decoding by ear. To create the final application for training, the Processing toolkit was chosen, since its key parameter when choosing a development tool has a simple writing syntax to increase the speed of writing code, as well as the ability of the environment to work with the communication channel of the microcontroller.

An investigation of Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis model dynamics with pseudo-recovery and psychological effect

Tuberculosis is one of the most pressing issues of the modern era, posing a severe health risk to humans in recent decades. This study proposes a Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis epidemic transmission model with psychological effects and pseudo-recovery. We consider a compartmental mathematical model in which the entire population is divided into four compartments based on their natural features. The model is validated, and parameter values are estimated using Indonesian data from 2002 to 2022. To investigate their epidemiological significance, we proved the positivity and boundedness of solutions, as well as the local and global stability of equilibria. Sensitivity analysis is used to find the most influential parameters with the most significant influence on the basic reproduction number, R0. The bifurcation procedure tools of the center manifold theory are used to conduct a bifurcation study. Mathematical conditions ensure the inferred event of forward bifurcation. We performed numerical simulations that support our theoretical findings.

Evolutionary Dynamics of Population Games With an Aspiration-Based Learning Rule.

Agents usually adjust their strategic behaviors based on their own payoff and aspiration in gaming environments. Hence, aspiration-based learning rules play an important role in the evolutionary dynamics in a population of competing agents. However, there exist different options for how to use the aspiration information for specifying the microscopic learning rules. It is also interesting to investigate under what conditions the aspiration-based learning rules can favor the emergence of cooperative behavior in population games. A new learning rule, called as "Satisfied-Cooperate, Unsatisfied-Defect", is proposed here, which is based on aspiration. Under this learning rule, agents prefer to cooperate when their income is satisfied; otherwise, they prefer the strategy of defection. We introduce this learning rule to a population of agents playing a generalized two-person game. We, respectively, obtain the mathematical conditions in which cooperation is more abundant in finite well-mixed, infinite well-mixed, and structured populations under weak selection. Interestingly, we find that these conditions are identical, no matter whether the aspiration levels for cooperators and defectors are the same or not. Furthermore, we consider the prisoner's dilemma game (PDG) as an example and perform numerical calculations and computer simulations. Our numerical and simulation results agree well and both support our theoretical predictions in the three different types of populations. We further find that our aspiration-based learning rule can promote cooperation more effectively than alternative aspiration-based learning rules in the PDG.

Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information

To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.

Building up a model family for inflammations

The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction–diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The classes are found by translating biological knowledge into mathematical conditions and the analysis of the models further constrains the classes. Numerical simulations allow comparing single models out of the model family with available qualitative information on the solutions from observations. The method provides insight into a hierarchical order of the mechanisms. The method is applied to the clinics for liver inflammation such as metabolic dysfunction-associated steatohepatitis or viral hepatitis where reasons for the chronification of disease are still unclear and time- and space-dependent data is unavailable.

Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Establishing a mapping between the emergent biological properties and the repository of network structures has been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance that promotes regulation in the presence of environmental disturbances. This paper presents a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation with respect to external disturbances of arbitrary magnitude. Based on the prior information about the network, we frame precise mathematical conditions for adaptation using nonlinear systems theory. We first deduce the mathematical conditions for perfect adaptation for constant input disturbances. Subsequently, we translate these conditions to specific necessary structural requirements for adaptation in networks of small size and then extend to argue that there exist only two classes of architectures for a network of any size that can provide local adaptation in the entire state space, namely, incoherent feed-forward (IFF) structure and negative feedback loop with buffer node (NFB). The additional positiveness constraints further narrow the admissible set of network structures. This also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The proposed method does not assume any explicit knowledge of the underlying rate kinetics, barring some minimal assumptions. Finally, we also discuss the infeasibility of certain IFF networks in providing adaptation in the presence of downstream connections. Moreover, we propose a generic and novel algorithm based on non-linear systems theory to unravel the design principles for global adaptation. Detailed and extensive simulation studies corroborate the theoretical findings.

Points of inflection of special eigenvalue functions as indicators of stiffness maxima/minima of proportionally loaded structures

The stiffness of a proportionally loaded structure may continuously increase or decrease. As a special exception, it may be constant. On the other hand, an initially stiffening (softening) structure may turn into a softening (stiffening) structure. At the load level of such a change the stiffness of the structure attains an extreme value. The task of this work is to present mathematical conditions for these load levels. Lack of them represents a void in the pertinent literature. The practical significance of the aforementioned changes is the one of indicators of the mechanical behavior to be expected after their occurrence. The second and the last author have recently presented a condition for the load level at which the stiffness of a proportionally loaded structure becomes a minimum value. It is given as d2(ℜ(χ1(λ)))/dλ2=0, representing the condition for a point of inflection of the real part of a complex eigenvalue function χ1(λ), where λ denotes a dimensionless load parameter. The underlying linear eigenvalue problem has two indefinite coefficient matrices, which is a necessary condition for complex regions of eigenvalue functions. These matrices are established with hybrid elements, available in a commercial finite element program. In the present work, d2(χ1(λ))/dλ2=0 is shown to be the condition for the load level at which the stiffness of a proportionally loaded structure attains a maximum value. The eigenvalue function concerned has no complex region. It is also shown that the displacement elements, which are the basis for their extension to the employed hybrid elements, are unable to indicate the load level at an extreme value of the stiffness.

The smart nanocarrier containing zein/starch co-biopolymers enhanced by graphitic carbon nitride; exploring opportunities in brain cancer treatment

In this investigation, we present an innovative pH-responsive nanocomposite designed to address challenges associated with using 5-Fluorouracil (5-FU) in cancer therapy. The nanocomposite containing zein (Z), starch (S), and graphitic carbon nitride (g-C3N4) macromolecules is synthesized by a water-in-oil-in-water (W/O/W) double emulsion technique, serving as a carrier for 5-FU. The S/Z hydrogel matrix's entrapment and loading efficiency are greatly improved by adding g-C3N4 nanosheets, reaching noteworthy values of 45.25 % and 86.5 %, respectively, for drug loading efficiency and entrapment efficiency. Characterization through FTIR and XRD validates the successful loading of 5-FU, elucidating the chemical bonding within the nanocomposite and crystalline characteristics. Structural analysis using FESEM, along with DLS and zeta potential measurements, reveals an average nanocomposite size of 193.48 nm, indicating a controlled structure, and a zeta potential of −42.32 mV, signifying a negatively charged surface. Studies on the in vitro release of drugs reveal that 5-FU is delivered more effectively and sustainably in acidic environments than in physiological circumstances. This highlights the fact that the created nanocarrier is pH-sensitive. Modeling release kinetics involves finding the right mathematical conditions representing underlying physicochemical processes. Employing curve-fitting techniques, predominant release mechanisms are identified, and optimal-fitting kinetic models are determined. The Baker kinetic model performed best at pH 7.4, indicating that the leading cause of the drug release was polymer swelling. In contrast, the Higuchi model was most accurate for drug release at pH 5.4, illuminating the diffusion and dissolution mechanisms involved in diffusion. To be more precise, the mechanism of release at pH 7.4 and 5.4 was anomalous transport (dissolution-controlled), according to the Korsmeyer-Peppas mathematical model. The pH-dependent swelling and degradation behavior of S/Z/g-C3N4@5-FU nanocomposite showed higher swelling and faster degradation in acidic environments compared to neutral conditions. Crucially, outcomes from the MTT test affirm the significant cytotoxicity of the 5-FU-loaded nanocomposite against U-87 MG brain cancer cells, while simultaneously indicating non-toxicity towards L929 fibroblast cells. These cumulative findings underscore the potential of the engineered S/Z/g-C3N4@5-FU as a productive and targeted therapeutic approach for cancer cells.

Non-linear impedance boundary condition from linear piecewise B-H curve applied to induction heating systems

Purpose This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model. Design/methodology/approach An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system. Findings A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements. Practical implications This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations. Originality/value In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.

Is the incumbent crying or laughing: when does the entrant adopt the market expansion entry strategy?

PurposeIt is only logical that a firm aims to make a profit after entering the market. However, some firms enter the market with the goal of market expansion and even burn money to pursue market share, which is counterintuitive in practice. To explore the theoretical foundations behind this rare phenomenon, this paper focuses on discussing the impact of the market expansion entry strategy on the entrant firm and the incumbent firm.Design/methodology/approachUsing a game theory model of a supply chain with an incumbent and an entrant, this paper explores the mathematical conditions for the entrant to adopt either the traditional or the market expansion entry strategy and investigates the incumbent’s benefits and losses under different entry strategies.FindingsThe results show that when the market-expansion effect and the selling price ceiling are moderate, the entrant firm always adopts the market expansion entry strategy, and the incumbent firm obtains a free ride from the entrant firm and benefits from it. The entire industry profits and the industry consumer surplus are increased. In particular, we further investigate the cases in which the incumbent firm has a first-mover advantage or there is a troublesome cost, and the results confirm the aforementioned conclusions.Originality/valueBy considering market share as the entrant’s goal, this paper contributes to the dual-purpose literature. Moreover, based on the model’s mathematical results, this paper offers relevant management insights for the entrant and its stakeholders in the e-commerce platform.

Visualizing entanglement in multiqubit systems

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus lies especially on ensembles of few qubits. There exist many powerful representations for single-qubit and multiqubit systems, such as the famous Bloch sphere and generalizations. Here, we utilize the dimensional circle notation as a representation of such ensembles, adapting the so-called circle notation of qubits and the idea of representing the n-particle system in an n-dimensional space. We show that the mathematical conditions for separability lead to symmetry conditions of the quantum state visualized, offering a new perspective on entanglement in few-qubit systems and therefore on various quantum algorithms. In this way, dimensional notations promise significant potential for conveying nontrivial quantum entanglement properties and processes in few-qubit systems to a broader audience, and could enhance understanding of these concepts as a bridge between intuitive quantum insight and formal mathematical descriptions. Published by the American Physical Society 2024

A Hierarchical approach for isolating sensor faults from un-stealthy attacks in large-scale systems

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L2−L∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (CSTR).

Dispersion Relations Alone Cannot Guarantee Causality.

We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation ω(k) always propagate outside the light cone unless ω(k)=a+bk. This implies that there is no notion of causality for individual dispersion relations since no mathematical condition on the function ω(k) (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This happens automatically in local theories of matter that are covariantly stable. Hence, we find that the need for nonhydrodynamic modes in relativistic fluid mechanics is analogous to the need for antiparticles in relativistic quantum mechanics.

Equivalent analysis model of a GaN LED used as a receiver

In general, visible light communication (VLC) uses LEDs as transmitters. However, LEDs can serve as receivers to construct a simple duplex VLC system that uses only two LEDs instead of one LED and one photo-diode (PD). There is a lack of effective equivalent analysis models for characterizing and evaluating the inherent behavioral characteristics of LEDs used as receivers. This paper presents an equivalent analysis model for GaN LEDs as receivers. First, based on the proposed receiving equivalent circuit model, a third-order signal transmission mathematical analysis model is established, revealing the transmission relationship between the photocurrent and output voltage. Further research is conducted on the impact of parameter changes on the bandwidth, and the model can be simplified into a first-order low-pass mathematical analysis model under specific conditions, providing theoretical support for improving the bandwidth of LED receiving applications. The experimental results also confirm the theoretical predictions. This research result holds significant importance for revealing the intrinsic mechanisms and the improved optical communication performance of LEDs for effective reception.

The QCD axion sum rule

We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides the η′). We determine the exact mathematical condition for an arbitrary N-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among the N axion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{N} $$\\end{document} at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associated N − 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.

Dynamics of collective cooperation under personalised strategy updates

Collective cooperation is essential for many social and biological systems, yet understanding how it evolves remains a challenge. Previous investigations report that the ubiquitous heterogeneous individual connections hinder cooperation by assuming individuals update strategies at identical rates. Here we develop a general framework by allowing individuals to update strategies at personalised rates, and provide the precise mathematical condition under which universal cooperation is favoured. Combining analytical and numerical calculations on synthetic and empirical networks, we find that when individuals’ update rates vary inversely with their number of connections, heterogeneous connections actually outperform homogeneous ones in promoting cooperation. This surprising property undercuts the conventional wisdom that heterogeneous structure is generally antagonistic to cooperation and, further helps develop an efficient algorithm OptUpRat to optimise collective cooperation by designing individuals’ update rates in any population structure. Our findings provide a unifying framework to understand the interplay between structural heterogeneity, behavioural rhythms, and cooperation.

Quantum simulation of Pauli channels and dynamical maps: Algorithm and implementation.

Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps (parametrized Pauli channels). A parametrized quantum circuit is employed to accommodate for dynamical maps. We also establish the mathematical conditions for an N-qubit transformation to be achievable using a parametrized circuit where only one single-qubit operation depends on the parameter. The implementation of the proposed circuit is demonstrated using IBM's quantum computers for the case of one qubit, and the fidelity of this implementation is reported.

Axisymmetric blockfold origami: a non-flat-foldable Miura variant with self-locking mechanisms and enhanced stiffness

Origami foldcores, especially the blockfold cores, have emerged as promising components of high-performance sandwich composites. Inspired by the blockfold origami, we propose the axisymmetric blockfold origami (ABO), which is composed of both rectangular and trapezoidal panels. The ABO inherits the non-flat-foldability of the blockfold origami, and furthermore, displays self-locking mechanisms and enhanced stiffness. The geometry and folding kinematics of the ABO are formulated with respect to the geometric parameters and the folding angle of the assembly. The mathematical conditions are derived for the existence of self-locking mechanisms. We perform compression test simulations to demonstrate enhanced stiffness and increased load-bearing capacity. We find that the existence of rectangular panels not only dominates the non-flat-foldability of the ABO, but also contributes to the enhancement of the stiffness. Our results suggest the potential applications of the ABO for building load-bearing structures with rotational symmetry. Moreover, we discuss the prospects of designing tightly assembled multi-layered origami structures with prestress induced by the mismatch of successive layers to enlighten future research.