Solution Of Model Research Articles

Exact analytical solution of the Flory-Huggins model and extensions to multicomponent systems.

The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory's ease of application. In this work, we derive an implicit analytical solution to the Flory-Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.

Multimodal deep learning using on-chip diffractive optics with in situ training capability

Multimodal deep learning plays a pivotal role in supporting the processing and learning of diverse data types within the realm of artificial intelligence generated content (AIGC). However, most photonic neuromorphic processors for deep learning can only handle a single data modality (either vision or audio) due to the lack of abundant parameter training in optical domain. Here, we propose and demonstrate a trainable diffractive optical neural network (TDONN) chip based on on-chip diffractive optics with massive tunable elements to address these constraints. The TDONN chip includes one input layer, five hidden layers, and one output layer, and only one forward propagation is required to obtain the inference results without frequent optical-electrical conversion. The customized stochastic gradient descent algorithm and the drop-out mechanism are developed for photonic neurons to realize in situ training and fast convergence in the optical domain. The TDONN chip achieves a potential throughput of 217.6 tera-operations per second (TOPS) with high computing density (447.7 TOPS/mm2), high system-level energy efficiency (7.28 TOPS/W), and low optical latency (30.2 ps). The TDONN chip has successfully implemented four-class classification in different modalities (vision, audio, and touch) and achieve 85.7% accuracy on multimodal test sets. Our work opens up a new avenue for multimodal deep learning with integrated photonic processors, providing a potential solution for low-power AI large models using photonic technology.

Numerical Performance of the Fractional Direct Spreading Cholera Disease Model: An Artificial Neural Network Approach

The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which provides more precise solutions as compared to the integer-order one. Real values based on the parameters can be obtained and one can achieve better results by utilizing these values. The mathematical form of the fractional direct spreading cholera disease is categorized as susceptible, infected, treatment, and recovered, which represents a nonlinear model. The construction of the dataset is performed through the implicit Runge–Kutta method, which is used to lessen the mean square error by taking 74% of the data for training, while 8% is used for both validation and testing. Twenty-two neurons and the log-sigmoid fitness function in the hidden layer are used in the stochastic neural network process. The optimization of BR is performed in order to solve the direct spreading cholera disease problem. The accuracy of the stochastic process is authenticated through the valuation of the outputs, whereas the negligible calculated absolute error values demonstrate the approach’s correctness. Furthermore, the statistical operator performance establishes the reliability of the proposed scheme.

Numerical Procedure for the Solution of Non-Linear Pulp Washing Models

Numerical Procedure for the Solution of Non-Linear Pulp Washing Models

A computational model for single cell Lamin-A structural organization after microfluidic compression.

In recent years, nuclear mechanobiology gained a lot of attention for the study of cell responses to external cues like adhesive forces, applied compression, and/or shear-stresses. In details, the Lamin-A protein-as major constituent of the cell nucleus structure-plays a crucial role in the overall nucleus mechanobiological response. However, modeling and analysis of Lamin-A protein organization upon rapid compression conditions in microfluidics are still difficult to be performed. Here, we introduce the possibility to control an applied microfluidic compression on single cells, deforming them up to the nucleus level. In a wide range of stresses (~1-102 kPa) applied on healthy and cancer cells, we report increasing Lamin-A intensities which scale as a power law with the applied compression. Then, an increase up to two times of the nuclear viscosity is measured in healthy cells, due to the modified Lamin-A organization. This is ascribable to the increasing assembly of Lamin-A filament-like branches which increment both in number and elongation (up to branches four-timelonger). Moreover, the solution of a computational model of differential equations is presented as a powerful tool for a single cell prediction of the Lamin-A assembly as a function of the applied compression.

Energy Management Strategy for Wind Solar Storage Microgrid Based on Improved Ant Lion Optimizer

The energy management of microgrids involves optimizing the capacity configuration, which significantly impacts the economic and stable operation of microgrids. This paper presents a control strategy for microgrid operation that effectively manages distributed power sources and energy storage to optimize capacity configuration. A mathematical optimization model for microgrid energy management is established considering minimum annual cost and optimal scale constraints. The traditional Ant Lion Optimizer (ALO) is improved by using dynamic weight coefficients and chaotic mapping to enhance the diversity of the population and improve the convergence of the algorithm. This can effectively avoid local optimal solutions and premature problems, and improve the convergence speed and search ability of the ALO algorithm. Based on this control strategy and improved ALO algorithm, simulations and tests were conducted using actual data from an independent microgrid, resulting in the optimal solution for the microgrid capacity allocation model. The case study results validate the practicality of the proposed microgrid operation control strategy as well as the superiority of the improved ant colony optimization algorithm.

Novel exact traveling wave solutions of Newton-Schrödinger system using Nucci reduction and Sardar sub-equation methods

The main theme of this piece of research is to tackle a coupled Newton-Schrödinger type model. Two analytical techniques namely, Nucci reduction method and Sardar sub-equation methods have been employed to scrutinize exact traveling wave solutions. Through the application of these approaches, various solitary and traveling wave solutions including bright, dark and singular periodic solitons, have been obtained. Further, we have not only discussed the physical depiction of specific solutions but have also visually presented them through two dimensional (2D), three dimensional (3D), and density plots utilizing relevant parameter values. The extracted solutions show that the proposed methods are effective, simple, and successful in pinpointing the exact solution of models in engineering, optics, and other nonlinear disciplines.

The trajectory of anxiety symptoms during the transition from childhood to young adulthood is predicted by IQ and sex, but not polygenic risk scores

AbstractBackgroundUnderstanding the factors that determine distinct courses of anxiety symptoms throughout development will better guide interventions. There are scarce data‐driven longitudinal studies, using multi‐modal predictors, investigating the chronicity of anxiety symptoms from childhood to young adulthood, particularly in a middle‐income country.Methods2033 youths (ages 6–14 years [Mean age = 10.4 ± 1.94) at Baseline] were enrolled in the Brazilian High‐Risk Cohort for Mental Conditions longitudinal study, and assessed at three timepoints, between 2010 and 2019, using the Screen for Child Anxiety Related Disorders. Confirmatory Factor Analysis provided input to Growth Mixture Models to identify the best fitting trajectory model. Multinomial logistic regression analyses tested the effects of intelligence quotient (IQ), environmental factors and polygenic risk scores on internalizing symptomatology within trajectory class membership.ResultsThe best model solution identified three classes: high‐decreasing, moderate/low‐stable and low‐increasing symptoms over time. The high‐decreasing class showed a higher incidence of anxiety symptoms at the second time point (Mean age = 13.8 ± 1.93); while anxiety symptoms were highest in the low‐increasing class at the third timepoint (Mean age = 18.35 ± 2.03). Further, lower IQ predicted membership in the high‐decreasing trajectory class (OR = 0.68, 95% CI [0.55, 0.85]), while higher IQ predicted membership in the low‐increasing trajectory class (OR = 1.95, 95% CI [1.42, 2.67]). Finally, females were more likely than males to be in the low‐increasing trajectory class. Polygenic risk scores were not associated with anxiety trajectory class membership.ConclusionRecognizing that anxiety symptoms follow diverse paths over time will allow for more effective intervention strategies. Specifically, interventions could accommodate children for greater anxiety risk in early childhood (i.e., lower IQ) versus late adolescence (i.e., higher IQ). That said, the emotional needs of girls in late adolescence should be monitored, regardless of their cognitive abilities or high achievements.

The STEP-ONE program (Supportive Training and Essential Preparation for Optimal Nursing Education) - what have we done and what will we do in the STEP-TWO edition?

Abstract Introduction The STEP-ONE program was a significant initiative designed to enhance the skills and knowledge of nurses specializing in heart failure care in Central and Eastern Europe, and the Baltic countries (CEE-BA). Purpose Its importance lies in addressing the crucial role of nurses in heart failure management, an area often overlooked in these regions. By training nurses to provide optimal, integrated care, the program aims to improve patient outcomes and reduce hospitalizations. The number of nurses who participated in the program is not specified, but its impact is likely substantial in advancing heart failure care. Continuing the program as the STEP-TWO edition is planned to be updated of nurses and patients materials according to ESC HF 2023 guidelines6, taking into account the profile of the patient with HFrEF, HFmREF, HFimEF, HFpEF and taking into account the implementation of pilot projects: (1a) Assessment of HFpEF risk7 and recommendations for medical staff regarding further diagnostics; (1b) Analysis of recommended therapies according to guidelines; (2) Pilot training Program center Poland centers- CEE-BA; (3) Pilot research programs - 1a and 1/b in 2-3 centers (fig.1). All of the activities undertaken in the program are intended to improve care for heart failure patients and can be seen as a model solution for providing qualified personnel in the European countries. Conclusions The STEP ONE educational program was developed with the participation of the medical community, especially nurses caring for HF patients. Educational materials for nurses and patients, as well as an educational program, were prepared and implemented in Poland and the region of CEE-BA. During the second phase, an updated materials with the 2023 guidelines on HF will be prepared. A pilot study will evaluate the impact of educating HF nurses on patient risk assessment of HFPEF and on identifying patients who do not have optimal therapy according to GDMT. Optimization of the HF patient pathway at the pilotage centers of the program and collaboration between HF nurses and cardiologists will be sought. Moreover, the STEP-TWO program will include preparing educational materials focused and dedicated not only on patients but also on caregivers.

Large strain consolidation of soft soils with partially penetrating PVDs: Analytical solutions incorporating variable well resistance

The large-strain geometric assumptions and nonlinear compressibility and permeability have significant effects on the consolidation of soft soils with high compressibility. However, analytical solutions for large-strain nonlinear consolidation of soft soils with partially penetrating PVDs have been rarely reported in the literature. A double logarithmic model is adopted to describe the nonlinear compressibility and permeability of soft soils with high compressibility, and a large-strain consolidation model for soft soils with partially penetrating PVDs under the condition that the excess pore water pressure at the interface between the improved and unimproved layers is equal is established based on Gibson’s large-strain consolidation theory. The analytical solution for the large-strain nonlinear consolidation model for soft soils with partially penetrating PVDs is obtained. The reliability of the analytical solution obtained in this study is verified by comparing it with the existing solutions under different conditions, and the maximum deviation between the two methods does not exceed 5 %. On this basis, consolidation behaviors of soft soils with partially penetrating PVDs under different conditions were analyzed by extensive calculations. Finally, the proposed analytical solution for the large strain consolidation model is applied to the settlement calculation of the Bachiem Highway Project, which further demonstrates the applicability of the consolidation model.

Derivatization, solid-phase microextraction and gas chromatography for determination of dialdehydes—biomarkers of oxidative stress

Dialdehydes are often used as biomarkers, molecules of interest for diagnosis, medical studies, and scientific research. A well-known example is malondialdehyde, which is a biomarker of oxidative stress formed during lipid peroxidation. We used combination of derivatization with O-(1,2,3,4,5)-pentafluorobenzylhydroxylamine, headspace solid-phase microextraction and gas chromatography with flame ionization detector for the analysis of dialdehydes. This combination allows to ensure the stability of analytes by derivatization, to separate them from the matrix, to preconcentrate by solid-phase microextraction, and to perform determination of dialdehydes. All the parameters affecting sensitivity and selectivity (pH and time of derivatization, sorption time, temperature of sorption, salt addition) were studied specifically for malondialdehyde, glyoxal, and methylglyoxal. The addition of salting-out agent resulted in decrease in the signal; therefore, a possible matrix effect was tested using simulated body fluid as model solution with ion composition similar to blood plasma. Established conditions for this method for dialdehydes showed 84–102% recovery in the model solution and allowed to reach the limits of quantification 0.2–0.8 μmol/L, which is low enough for the analysis of real samples. This method has the potential to be automated and is environmentally friendly because it does not require organic solvents and single-used filters or cartridges.

Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model

The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), particularly in the context of HIV infection treatment, and the innovative use of GBPs and Lagrange multipliers in solving the fractional hematopoietic stem cells model (FHSCM). The aim of the study is to introduce an optimization algorithm for approximating the solution of the FHSCM using GBPs and Lagrange multipliers and to provide a comprehensive exploration of the mathematical techniques employed in this context. The research methodology involves formulating operational matrices for fractional derivatives of GBPs, conducting a convergence analysis of the proposed method, and demonstrating the accuracy of the method through numerical simulations. The major conclusion is the successful introduction of GBPs in the context of the FHSCM, featuring innovative control parameters and a novel optimization technique. The study also highlights the significance of the proposed method in providing accurate solutions for the FHSCM, thus contributing to the field of mathematical modeling in biological and medical research.

An approximate analytical solution of a 4-DOF variable-length pendulum model

An approximate analytical solution of a 4-DOF variable-length pendulum model

Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model

In the present work, a relativistic relation that connects the difference of interacting and noninteracting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is derived. We show that the difference of integrated finite volume correlation functions converges rapidly to its infinite volume limit as the size of the periodic box is increased. The fast convergence of our proposed formalism is illustrated by analytic solutions of a contact interaction model, the perturbation theory calculation, and also the Monte Carlo simulation of a complex ϕ4 lattice field theory model. Published by the American Physical Society 2024

Linking hypothetical extraction, the accumulation of production factors, and the addition of value

AbstractIn industrial ecology, approaches have been developed to analyze the contribution of specific sectors to environmental impacts within supply chains. In economics, a range of methods addresses the forward linkage (use of output) and backward linkage (dependency on inputs) of sectors, and the analysis of key sectors. This article offers a formal investigation of the relationship between these. It shows that both the analysis of supply chain impacts and of intersectoral linkages can be seen as special cases of a more general hypothetical extraction method (HEM). In HEM, sectors' role is assessed as the effect of their removal on the input–output model's solution. HEM also allows for the (partial) extraction of individual transactions. HEM thus offers a flexible approach to assessing the contribution of one or several sectors, or transactions, or parts thereof, to value added or footprint of any final demand. It can be applied to study the environmental footprints of companies or intermediate products, the contribution of certain inputs to sectors, or the potential impact of disruptions of supply chains on producers and consumers. In this article, the price model for HEM is introduced to identify the contribution of the extracted (target) sectors to the price or unit footprint of a commodity.

Linking hypothetical extraction, the accumulation of production factors, and the addition of value

AbstractIn industrial ecology, approaches have been developed to analyze the contribution of specific sectors to environmental impacts within supply chains. In economics, a range of methods addresses the forward linkage (use of output) and backward linkage (dependency on inputs) of sectors, and the analysis of key sectors. This article offers a formal investigation of the relationship between these. It shows that both the analysis of supply chain impacts and of intersectoral linkages can be seen as special cases of a more general hypothetical extraction method (HEM). In HEM, sectors' role is assessed as the effect of their removal on the input–output model's solution. HEM also allows for the (partial) extraction of individual transactions. HEM thus offers a flexible approach to assessing the contribution of one or several sectors, or transactions, or parts thereof, to value added or footprint of any final demand. It can be applied to study the environmental footprints of companies or intermediate products, the contribution of certain inputs to sectors, or the potential impact of disruptions of supply chains on producers and consumers. In this article, the price model for HEM is introduced to identify the contribution of the extracted (target) sectors to the price or unit footprint of a commodity.

Novel exact traveling wave solutions of Newton-Schr"odinger system using Nucci reduction and Sardar sub-equation methods

Abstract The main theme of this piece of research is to tackle a coupled Newton-Schrödinger type model. Two analytical techniques namely, Nucci reduction method and Sardar sub-equation methods have been employed to scrutinize exact traveling wave solutions. Through the application of these approaches, various solitary and traveling wave solutions including bright, dark and periodic solitons, have been obtained. Further, we have not only discussed the physical depiction of specific solutions but have also visually presented them through 3D, 2D and density plots utilizing relevant parameter values. The extracted solutions show that the proposed methods are effective, simple, and successful in pinpointing the exact solution of models in engineering, optics, and other nonlinear disciplines.

Geophysical and numerical approaches to solving the mechanisms of landslides triggered by earthquakes: A case study of Kahramanmaraş (6 February, 2023)

Many landslides occurred in the 11 Turkish provinces affected by the earthquakes centered in Kahramanmaraş in February 2023, and many people lost their lives due to those landslides. To reduce the risks and hazards brought on by landslides induced by earthquakes, it is essential to identify the mechanisms causing landslides to arise in such situations. In this study, the geological strength index and both seismic refraction tomography and electrical resistivity tomography (ERT) geophysical methods were used to determine the failure mechanism of layered sedimentary units defined as flysch (claystone-siltstone-sandstone-marl). The shear strength reduction finite element method (SSR-FEM) was used with the RS2 computer program for model solutions. One of the geophysical methods, ERT, facilitated an interpretation of the cyclic failure mechanism that occurs in flysch, and it was found to be congruent with numerical models. Landslide slip circle depth, water-saturated layers, and resistivity values were determined with the ERT method. Seismic methods were employed to determine the velocity values (Vp, Vs) of the landslip mass. These velocity data, along with the elasticity modulus and Poisson ratios derived from them, were utilized in our numerical model. In the maximum shear strength and horizontal displacement analyses performed on the section line determined before the landslide, the natural state and the situation under the influence of groundwater were examined and the strength reduction factor (SRF) was determined as 1.35 and 1.24, respectively. In an evaluation conducted under the influence of the maximum horizontal ground acceleration (0.22 g) determined by taking into account the seismicity of the study area, it was concluded that instability occurred in the flysches and the SRF value was 0.72. An important finding of this study is that the results of geophysical methods used to determine the lithological properties of sedimentary rock masses and understand the causes of landslides align closely with those of numerical analysis methods, providing high accuracy. These methods also support new approaches, particularly in identifying landslip boundaries and detecting areas with high water saturation. It has been discovered that earthquakes actively contribute to the instability of these kinds of soils.

Thermomechanical effects during air blast freezing of fruit pulp model solutions with different sucrose concentrations in metal drums

The strains on the metal drums surfaces caused by the ice volumetric expansion during the freezing of model solutions of fruit pulps were evaluated by extensometers. 200 kg of model solutions of 0.5% k-carrageenan (w/v) added 0.5%, 10% or 20% (w/v) sucrose into metal drums were frozen in air blast freezer at −25 °C. Strain gauge sensors were installed on the side surface and bottom of the drums in a balanced Wheatstone bridge circuit. The resulting stresses and temperature profiles inside the packages were measured simultaneously. The non-uniform temperature distribution in the product was proven by IR thermography. There was reduction in the freezing temperature and stresses in the packages with the increase in the sucrose concentration. The restricted surfaces, preventing the expansion of the ice, yielded great stresses in the frozen solutions and induced cracking in the free surfaces of the solutions, especially in the systems with lower concentrations.

Symmetry-Optimized Dynamical Analysis of Optical Soliton Patterns in the Flexibly Supported Euler–Bernoulli Beam Equation: A Semi-Analytical Solution Approach

This study employs spatial optimization principles to investigate the nonlinear vibration of a flexibly supported Euler–Bernoulli beam, a (1 + 1)-dimensional system subjected to axial loads. The modified Khater method, a crucial tool in mechanical engineering, is utilized to analyze analytical solutions, which include a symmetric spatial representation of the waveform as an integral part of each solution. Notably, periodic soliton solutions for the nonlinear model closely align with numerical and approximate analytical solutions, demonstrating the accuracy of our modeling approach. Density diagrams, contour diagrams, and Poincaré maps depicting the obtained analytical solutions are presented to elucidate their accuracy and provide visual confirmation of the optimized engineering model’s physical significance. The planar dynamical system is derived through the Galilean transformation by employing mathematical models and appropriate parameter values, thereby further refining problem understanding. Sensitivity analysis is conducted, and phase portraits with equilibrium points are illustrated by analyzing a special case of the investigated dynamical system, emphasizing its symmetrical properties. Lastly, we perform a global analysis to identify periodic, quasi-periodic, and chaotic behaviors, with an extra weak forcing term confirmed by Poincaré maps and a two-dimensional symmetric basin of the largest Lyapunov exponent.