Rigorous Theoretical Model Research Articles

Beyond four dimensions: An extended study of f(R,T) theory with multidimensional metric

The present communication explores [Formula: see text]-dimensional cosmological models within the framework of the [Formula: see text] theory. The exploration is motivated by Kaluza–Klein theory, where the existence of extra dimensions becomes a focal point in understanding the fundamental forces of the universe. A cosmological model has been constructed by assuming Fractional quadratic deceleration parameter. [Formula: see text] and [Formula: see text] provide a crucial link between theoretical predictions and empirical observations. Through rigorous mathematical analysis and theoretical modeling, we investigate the implications of this extended gravitational theory on cosmic evolution and the structure of spacetime. Our findings shed light on the interplay between geometry, matter and gravitational dynamics in multidimensional space, offering new insights into the nature of gravity and cosmological phenomenon.

Millimeter accuracy depth estimation in concrete using smartphone-equipped handheld GPR and hyperbolic curve fitting with antenna distance consideration

In the management and maintenance of structural facilities, knowing the cover thickness of rebar and the depth of buried objects is of paramount importance. Currently, Smartphone-Equipped Handheld Ground Penetrating Radars (GPR) are primarily used for detecting rebar, yet the Electromagnetic Induction (EMI) method remains the sole available technique for determining the cover thickness of rebar. This necessitates the use of two separate devices to understand the subsurface condition of rebar. In this study, we introduce a new algorithm that utilizes Hyperbolic Curve Fitting to determine depth and relative permittivity from reflection images derived from a single GPR measurement, using metal depth estimation as an exemplar. Our contributions include the automatic detection of the hyperbola's centerline before curve fitting, separation of the hyperbola into left and right for enhanced fitting accuracy by removing points near the vertex, and incorporating a rigorous theoretical model that took into account the distance between the transmitting and receiving antennas, known as the inter-antenna distance. This algorithm had enabled us to meet the performance requirements for the EMI method as stipulated by the Japanese Society for Non-Destructive Inspection (JSNDI). Notably, our method retained its accuracy even at depths exceeding the 100 mm limitation of the EMI method.

Nitrogen Vacancy Modulation of Tungsten Nitride Peroxidase-Mimetic Activity for Bacterial Infection Therapy.

Bacterial infections claim millions of lives every year, with the escalating menace of microbial antibiotic resistance compounding this global crisis. Nanozymes, poised as prospective substitutes for antibiotics, present a significant frontier in antibacterial therapy, yet their precise enzymatic origins remain elusive. With the continuous development of nanozymes, the applications of elemental N-modulated nanozymes have spanned multiple fields, including sensing and detection, infection therapy, cancer treatment, and pollutant degradation. The introduction of nitrogen into nanozymes not only broadens their application range but also holds significant importance for the design of catalysts in biomedical research. The synergistic interplay between W and N induces pivotal alterations in electronic configurations, endowing tungsten nitride (WN) with a peroxidase-like functionality. Furthermore, the introduction of N vacancies augments the nanozyme activity, thus amplifying the catalytic potential of WN nanostructures. Rigorous theoretical modeling and empirical validation corroborate the genesis of the enzyme activity. The meticulously engineered WN nanoflower architecture exhibits an exceptional ability in traversing bacterial surfaces, exerting potent bactericidal effects through direct physical interactions. Additionally, the topological intricacies of these nanostructures facilitate precise targeting of generated radicals on bacterial surfaces, culminating in exceptional bactericidal efficacy against both Gram-negative and Gram-positive bacterial strains along with notable inhibition of bacterial biofilm formation. Importantly, assessments using a skin infection model underscore the proficiency of WN nanoflowers in effectively clearing bacterial infections and fostering wound healing. This pioneering research illuminates the realm of pseudoenzyme activity and bacterial capture-killing strategies, promising a fertile ground for the development of innovative, high-performance artificial peroxidases.

Optimal chonsei to monthly rent conversion choice given borrowing constraints

Chonsei, an exceptional but prevalent housing rental system in the Republic of Korea, functions as private loans between individuals, and its implicit interest rate is called the “chonsei to monthly rent conversion rate”. Although the chonsei to monthly rent conversion rate is much higher than the interest rate of savings accounts or mortgage loans, making chonsei a more expensive channel of financing, chonsei remains a dominant type of rent in Korea. This study provides a novel theoretical model in a continuous-time portfolio selection framework that allows a lessor, given borrowing constraints, to optimally choose between chonsei and monthly rent contracts to show a possible solution to this situation. We investigate the optimal choice between chonsei and the monthly rent of lessors using a rigorous theoretical model and find a closed-form solution to the model. We analyze how credit availability in the banking sector affects the choice problem, showing that the lessor may prefer the chonsei contract over the monthly rent contract, given the borrowing limit from a bank. In addition, we analyze the impact of other major factors, such as the market price of risk, the amount of chonsei deposit, the monthly rental rate, and the income rate, on the lessor’s optimal decision between chonsei and monthly rent.

Size-dependent buckling in freestanding films driven by flexoelectricity

The flexibility in recently developed freestanding oxide films makes them fertile for exploring buckling-based flexible electronic devices at nanoscale. However, the rigorous flexoelectric theoretical model has not been established for accurately describing the buckling in a delamination film-substrate system yet. In this paper, we establish an electromechanical model by taking flexoelectricity into account to investigate the buckling properties of freestanding films. The results demonstrate the strain gradient of up to 106 m−1 in buckling films induces a giant flexoelectric effect. The flexoelectricity significantly suppresses the buckling deformation, of which the critical strain increases nearly tenfold as well as the buckling amplitude reduces by half. Meanwhile, flexoelectricity drives a size-dependent buckling behavior that differs from classical elastic buckling, in which the films with a smaller size exhibit a larger buckling resistance. These theoretical findings are well-confirmed experimentally. This work highlights the critical role of flexoelectricity in buckling films at nanoscale and provides guidelines for the design of buckling film-based flexoelectric devices.

Machine Learning

Abstract: Machine learning refers to the study and development of machine learning algorithms and techniques at a conceptual level, focusing on theoretical foundations, algorithmic design, and mathematical analysis rather than specific implementation details or application domains. It aimsto provide a deeper understanding of the fundamental principles and limitations of machine learning, enabling researchers to develop novel algorithms and advance the field. In abstract machine learning, the emphasis is on formalizing and analyzing learning tasks, developing mathematical models for learning processes, and studying the properties and behavior of various learning algorithms. This involves investigating topics such as learning theory, statistical learning, optimization, computational complexity, and generalization. The goalis to develop theoretical frameworks and mathematical tools that help explain why certain algorithms work and how they can be improved. Abstract machine learning also explores fundamental questions related to the theoretical underpinnings of machine learning, such as the trade-offs between bias and variance, the existence of optimal learning algorithms, the sample complexity of learning tasks, and the limits of what can be learned from data. It provides a theoretical foundation for understanding the capabilities and limitations of machine learning algorithms, guiding the development of new algorithms and techniques. Moreover, abstract machine learning serves as a bridge between theory and practice, facilitating the transfer of theoretical insights into practical applications. Theoretical advances in abstract machine learning can inspire new algorithmic approaches and inform the design of real-world machine learning systems. Conversely, practical challenges and observations from realworld applications can motivate and guide theoretical investigations in abstract machine learning. Overall, abstract machine learning plays a crucial role in advancing the field of machine learning by providing rigorous theoretical frameworks, mathematical models, and algorithmic principles that deepen our understanding of learning processes and guide the development of more effectiveand efficient machine learning algorithms.

A multidimensional interpretation of Marxist globalization theory based on decentralized internet

Abstract To achieve a multidimensional interpretation of Marxist globalization theory, this paper provides a fecundation network facility based on a decentralized internet, thus overcoming various drawbacks of the network where traditional spatial services are located. In the Marxist theory of globalization, the rise from concrete rigor to abstract rigor is an important dialectical transformation of materialist epistemology. It is implied that Marx, based on the principle of mathematical expression of intuition and detail, refined, and deepened the paradigm itself through mathematical tools and mathematical methods, and used mathematical ideas to condense the theory of political economy, making the property of precision reflected in the logic of the paradigm. The 3PL model is established and the basic principles are accurately understood and grasped from mathematical logic according to the labor theory of value, surplus value theory and reproduction theory in Marxism, which provides an important generative logic for constructing a mathematical paradigm of Marxist political economy. The results of the study show that the output efficiency and benefits of fully cooperative networks (L = 0.92, Q = 281.5), after a long period of competition makes the output of the network less efficient, which in turn makes the network as a whole obtain lower returns (L = 0.73, Q = 96.18). In a competitive coexistence network structure, although there are competitive relationships at the core firm level, the network is not greatly affected by this (L = 0.83, Q = 202.92) instead, it will break the monopoly alliance and enliven the local economy. By constructing a rigorous and sophisticated mathematical and theoretical model, the theory of political economy can be made more abstract and scientific, and the analytical and explanatory power of the theory of political economy can be improved.

Creativity

This paper explores how adaptive creativity is continuously generated and sustained in living systems. The philosophical frame and motivations for this investigation will be introduced by juxtaposing an actual creative process with current cybernetic efforts to automate creativity. Past and present process philosophers that have critiqued the implicit commitments of these contemporary techniques will set the stage for further investigations. The litmus test of progress in this investigation will be measured against the extension of two concepts: virtuality, as introduced by Gilbert Simondon (On the Mode of the Existence of Technical Objects), and relevant noise, as introduced by Bacigalupi (“Semiogenesis: A Dynamic System Approach to Agency and Structure”). To refine the concepts of virtuality and relevant noise for our purposes, a rigorous theoretical model will be proposed whose intent is to explain veritable unbounded creativity. This model will then serve as a heuristic lens to explore additional extant models, such as the Kuramoto model (Strogatz), that are used to explain empirical observations of adaptive and creative behaviors in a diversity of biological phenomena. Based on these models of biological creativity and the critique of the contemporary cybernetic project, this paper will conclude by outlining the ethical implications of our culture’s current commitments to a cybernetic world view and how we might evolve beyond it.

In-Plane Rotation of Prolate Colloids Adhered to a Planar Substrate in the Presence of Flow.

Micron-size spherical polystyrene colloidal particles are mechanically stretched to a prolate geometry with desirable aspect ratios. The particles in an aqueous medium with specific ionic concentration are then introduced into a microchannel and allowed to settle on a glass substrate. In the presence of unidirectional flow, the loosely adhered particles in the secondary minimum of surface interaction potential are easily washed off, but the remnant in the strong primary minimum preferentially aligns with the flow direction and exercises in-plane rotation. A rigorous theoretical model is constructed to account for filtration efficiency in terms of hydrodynamic drag, intersurface forces, reorientation of prolate particles, and their dependence on flowrate and ionic concentration.

Comparative Energetics of Various Membrane Distillation Configurations and Guidelines for Design and Operation

This paper presents a comparative performance study of single-stage desalination processes with major configurations of membrane distillation (MD) modules. MD modules covered in this study are (a) direct contact MD (DCMD), (b) vacuum MD (VMD), (c) sweeping gas MD (SGMD), and (d) air gap MD (AGMD). MD-based desalination processes are simulated with rigorous theoretical MD models supported by molecular thermodynamic property models for the accurate calculation of performance metrics. The performance metrics considered in MD systems are permeate flux and energy efficiency, i.e., gained output ratio (GOR). A general criterion is established to determine the critical length of these four MDs (at fixed width) for the feasible operation of desalination in a wide range of feed salinities. The length of DCMD and VMD is restricted by the feed salinity and permeate flux, respectively, while relatively large AGMD and SGMD are allowed. The sensitivity of GOR flux with respect to permeate conditions is investigated for different MD configurations. AGMD outperforms other configurations in terms of energy efficiency, while VMD reveals the highest permeate production. With larger MD modules, utilization of thermal energy supplied by the hot feed for evaporation is in the order of VMD > AGMD > SGMD > DCMD. Simulation results highlight that energy efficiency of the overall desalination process relies on the efficient recovery of spent for evaporation, suggesting potential improvement in energy efficiency for VMD-based desalination.

Square Wave Voltcoulommetry of two-electron molecular electrocatalytic processes with adsorbed species. Application to the surface O2 reduction in acetonitrile at anthraquinone-modified glassy carbon electrodes

An adequate analysis of the performance and efficiency of a given multi-redox molecular electrocatalyst versus a particular substrate of interest requires the knowledge of the overall reaction pathway and the determination of the rate constants of the catalytic steps taking place. For this purpose, a theoretical model is presented for the Square Wave Voltcoulommetry response of surface-confined two-electron catalysts, that is, molecular species with two different redox states that can act in different electrocatalytic forms as a function of the applied potential. The rigorous theoretical model incorporates convective mass transport effects and non-idealities in the electrochemical behaviour of the immobilized redox probes. The results obtained have been applied to the study of the surface oxygen reduction in an aprotic medium (acetonitrile) at an anthraquinone-modified glassy carbon electrode. The charge-potential responses indicate that the reaction pathway involves two different catalytic routes due to the two reduction products of the anthraquinone moiety, that is, the semiquinone anion radical and the dianion. A Koutecky-Levich approach, combined with the fittings of the experimental responses to the theoretical expressions deduced here, has allowed us to obtain the values of the different thermodynamic (formal potential, interaction parameters, surface coverage) and kinetic (rate constant) parameters of the process.

Radiative Recombination Studies for Bare Lead Ions Interacting with Low-Energy Electrons

X-ray emission as a result of radiative recombination (RR) at threshold energies in the electron cooler of CRYRING@ESR was investigated for decelerated bare lead ions at a beam energy of 10 MeV/u. The recorded spectra are dominated by characteristic transitions in Pb81+, namely, the Lyman, Balmer and Paschen series, as a result of decay cascades from high-n states that are preferentially populated by the RR processes. In addition, a rigorous theoretical model is applied for the interpretation of measured X-ray spectra, and shows good agreement.

Probing ultra-fast dephasing via entangled photon pairs.

We demonstrate how the Hong-Ou-Mandel (HOM) interference with polarization-entangled photons can be used to probe ultrafast dephasing. We can infer the optical properties like the real and imaginary parts of the complex susceptibility of the medium from changes in the position and the shape of the HOM dip. From the shift of the HOM dip, we are able to measure 22 fs dephasing time using a continuous-wave (CW) laser even with optical loss > 97 %, while the HOM dip visibility is maintained at 92.3 % (which can be as high as 96.7 %). The experimental observations, which are explained in terms of a rigorous theoretical model, demonstrate the utility of HOM interference in probing ultrafast dephasing.

Effect of rotation in NMR diffusion experiments on micron-sized particles: A generalized theoretical treatment

We have recently developed an analytical framework to interpret the results of pulsed field gradient (PFG) NMR experiments on solution samples of micron-sized amyloid fibrils [Angew. Chem. Int. Ed. 60 (2021) 15445–15451. https://doi.org/10.1002/anie.202102408]. Here we generalize this result by reporting a rigorous theoretical model of such experiments, implemented in a form of efficient computational scheme. In particular, the new treatment fully accounts for the anisotropy of fibrils’ translational diffusion and takes into consideration the finite length of the gradient pulses. The results hold not only for the historic spin-echo sequence, but also for the widely used stimulated echo experiment. We have found that fibrils’ rotation can attenuate the echo by a factor comparable with that of translation. However, contrary to some recent claims, the rotational mechanism cannot lead to an apparent fast-diffusion situation.

Research on the Design of Accompanying Products for the Mentally Retarded Elderly Based on AHP

As the number of elderly patients with dementia is increasing year by year, accompanying products for the elderly with dementia are becoming more and more important. Senile dementia has become a major disease that affects countries around the world and, at the same time, it has brought enormous pressure on social care. Therefore, this research aims to obtain a new set of design methods for dementia elderly care products by introducing the combination of AHP and fuzzy evaluation methods and applying them to design examples. And then break through the existing design path of accompanying products for the elderly with dementia, and relieve the social burden. This study takes the intelligent care robot for the elderly with dementia as an example. Due to the particularity of user groups, this article proposed a design method for elderly care products that integrates mathematical theoretical models. This design method is convenient for designers to have a more accurate data reference when designing and positioning, and summarizing the supporting product design scheme that can better meet the actual needs of the elderly with dementia. Through SET factors to analyze the driving force of demand for dementia elderly care products, and combined with a questionnaire survey to establish the design requirements of dementia elderly care products for analysis of hierarchy process, it effectively defines the design demand attributes of dementia elderly intelligent care robots. The research results are applied to the design of the intelligent accompanying care robot for the demented elderly, the comprehensive fuzzy evaluation of the design scheme is carried out, and the direction of further optimization of the scheme is obtained. This article proposed a design method for accompanying care products for the elderly with dementia by combining F-AHP (Fuzzy Comprehensive Evaluation Method and Analytic Hierarchy Process). This design method is based on a rigorous mathematical theoretical model. Compared with the traditional design method, this research focused on quantitative analysis and evaluation of the actual design requirements of the dementia elderly care products and had more accurate design priority data reference in the scheme design. The research results show that based on the combination of F-AHP, this article redefines the design path of accompanying products for the elderly with dementia, and concludes that the functions that need to be improved and optimized in the future of intelligent accompanying robots for the elderly with dementia are mainly: executive ability training, computing ability training, and observation ability training. At the same time, the design process of the intelligent escort robot for the elderly with dementia can also be applied to the design of intelligent elderly products, which can improve the service experience of intelligent elderly products in a targeted manner.

Nuclear spin quantum memory in silicon carbide

Transition metal (TM) defects in silicon carbide (SiC) are a promising platform for applications in quantum technology. Some TM defects, e.g. vanadium, emit in one of the telecom bands, but the large ground state hyperfine manifold poses a problem for applications which require pure quantum states. We develop a driven, dissipative protocol to polarize the nuclear spin, based on a rigorous theoretical model of the defect. We further show that nuclear-spin polarization enables the use of well-known methods for initialization and long-time coherent storage of quantum states. The proposed nuclear-spin preparation protocol thus marks the first step towards an all-optically controlled integrated platform for quantum technology with TM defects in SiC.

Optical spatial filtering with plasmonic directional image sensors.

Photonics provides a promising approach for image processing by spatial filtering, with the advantage of faster speeds and lower power consumption compared to electronic digital solutions. However, traditional optical spatial filters suffer from bulky form factors that limit their portability. Here we present a new approach based on pixel arrays of plasmonic directional image sensors, designed to selectively detect light incident along a small, geometrically tunable set of directions. The resulting imaging systems can function as optical spatial filters without any external filtering elements, leading to extreme size miniaturization. Furthermore, they offer the distinct capability to perform multiple filtering operations at the same time, through the use of sensor arrays partitioned into blocks of adjacent pixels with different angular responses. To establish the image processing capabilities of these devices, we present a rigorous theoretical model of their filter transfer function under both coherent and incoherent illumination. Next, we use the measured angle-resolved responsivity of prototype devices to demonstrate two examples of relevant functionalities: (1) the visualization of otherwise invisible phase objects and (2) spatial differentiation with incoherent light. These results are significant for a multitude of imaging applications ranging from microscopy in biomedicine to object recognition for computer vision.

Quantitative analysis of the electrochemical performance of multi-redox molecular electrocatalysts. A mechanistic study of chlorate electrocatalytic reduction in presence of a molybdenium polyoxometalate

The quantification of the performance efficiency of a given molecular electrocatalyst versus a particular substrate of interest requires the determination of the rate constants of the catalytic steps taking place in the overall reaction pathway. In this paper, a theoretical model is presented for the quantitative analysis of the voltammetric response of multi-redox catalysts, that is, a molecular species with different redox states that can act in different electrocatalytic forms as a function of the applied potential. The rigorous theoretical model presented incorporates mass transport effects and it is applicable to disc electrodes of any size. As a model system, the electro-reduction of the anion chlorate by the polyoxometalate PMo12O403- (POM) is analysed at gold electrodes. The overall process implies ten charge transfer steps and three different two-electron catalytic processes, the formal potentials and rate constants of which are accurately determined, respectively. The logarithm of the rate constants for the three catalytic steps follows a linear relationship with the average formal potentials of the two-electron charge transfer processes. A comparison with previous efforts devoted to the characterisation of electrocatalytic responses is also carried out, pointing out the advantages of a rigorous solution for this problem.

Circular Dichroism Second-Harmonic Generation Imaging of KTiOPO4 Nanocrystal Through Stratified Media.

Potassium titanyl phosphate (KTiOPO4, KTP) particle of nanometric size (nano-KTP) is an attractive material for nonlinear microscopy, and the optimized growth of large-size KTP single crystals has numerous applications for efficient frequency conversion in laser technology. Its three-dimensional orientation and nanoscale morphology are important for growth optimization. In this paper, we introduce an imaging technique based on circular dichroism second-harmonic generation (CD-SHG) to characterize the 3D distribution of KTP nanocrystal. A rigorous theoretical model of CD-SHG imaging for nano-KTP through stratified media is demonstrated. Circular dichroism analysis is used to probe the orientation of 3-axis with respect to the optical observation axis. The research results show that the azimuthal angle of the peak value (SHG) or valley value (CD-SHG) is strongly related to the excitation polarization when the KTP sample is excited by different circular polarizations. Importantly, the refractive index mismatches and the imaging depth also affect the azimuthal angle. Thus, the proposed framework enables a more precise quantitative analysis of the CD-SHG signal of KTP.

Design and analysis of a compact solar concentrator tracking via the refraction of the rotating prism

The area for the solar energy utilization in the building is limited. With this in mind, a compact solar collector which integrated the prism and semi-parabolic trough mirror is proposed for the efficiently solar energy collecting in limited space. The prism is rotated to track the sun and keep the emitted sunlight perpendicular to the aperture of semi-parabolic trough mirror. The sunlight from the prism is then reflected and concentrated by semi-parabolic trough mirror and finally absorbed by the receiver tube. Based on the rigorous theoretical model, the tracking strategy is proposed and verified, which indicate that the sun could be tracked exactly and the tracking strategy is effective in the condition of non-parallel and multi-spectrum solar radiation. The geometric concentrating ratio, geometric parameters and the row arrangement of the proposed solar collector are all optimized. The results show that the annual solar-to-thermal efficiency evaluated by land area of the proposed solar collector is up to 41.1%, which is 6.7 and 17.6 percent points higher than those of parabolic trough and flat plate collectors, respectively. With the performance advantage in the solar collecting within limited space, the proposed solar collector could provide a promising approach for the solar energy utilization in the building.