Zeroth Order Research Articles

Homogenization and Phase Separation with Space Dependent Wells: The Subcritical Case

A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are allowed to move and to have discontinuities. The zeroth and first order Gamma -limits are identified. The topology considered for the latter is that of two-scale, since it encodes more information on the asymptotic local microstructure. In particular, when the wells are non-constant, the first order Gamma -limit describes the contribution of microscopic phase separation, even in situations where there is no macroscopic phase separation. As a corollary, the minimum of the mass constrained minimization problem is characterized, and it is shown to depend on whether or not the wells are discontinuous. In the process of proving these results, the theory of inhomogeneous Modica Mortola functionals is strengthened.

Cascaded HfO2/SiO2 microstructure for symmetrical two-port beam dispersion

A new type of double-dielectric layer two-port beam splitter grating based on sandwich structure is proposed. This grating has the characteristic of zeroth order elimination. The structural parameters of the grating are optimized by the rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SAA) to achieve the best performance of the grating. For both TE and TM polarizations, the diffraction efficiencies of ±1st orders can reach 49.34% and 49.15%, respectively. Meanwhile, the efficiency of the zeroth order is about only 0.5% for both polarizations. This novel microstructure has the significant characteristic of zeroth order elimination. Moreover, this grating has a wide incident bandwidth and excellent manufacturing tolerance. The simplified modal method (SMM) is also used to study the specific process of energy coupling in the grating.

DETERIORATION KINETICS OF NEUTRALIZED RED FRUIT (Pandanus conoideus L.) OIL DURING STORAGE

This study’s goal was to obtain a kinetics model of neutralized red fruit oil (NRFO) quality change during storage. The NRFO was stored in dark bottles at 60 °C, 75 °C and 90 °C for ± 15 days to evaluate the quality. The results showed that the quality of NRFO decreased along with the increase in temperature and storage time. This was indicated by increasing moisture content, Free Fatty Acid (FFA), peroxide number, as well as decreasing of the total carotenoids and total tocopherols. The FFA content and peroxide number of NRFO increase followed the kinetics zeroth order model, with activation energy (Ea) of 6372 cal/moloK and 9954 cal/moloK, respectively. Meanwhile, the decrease in carotenoid and tocopherol content followed the kinetics first order model, with Ea 9581 cal/moloK and 14242 cal/moloK, respectively. Estimation of shelf life of NRFO was based on peroxide number equation. The shelf life of NRFO is 398.5 days or 13.3 months if it is stored at 20 °; and the shelf life is 277.6 days or 9.3 months if it is stored 30 °C.

Coherent states on the circle: semiclassical matrix elements in the context of Kummer functions and the Zak transformation

We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer’s confluent hypergeometric functions. Earlier, these expectation values have only been obtained by using suitable estimates. On the other hand, we consider the Zak transformation not only to map harmonic oscillator coherent states to coherent states on the circle as it has been discussed before, but we also use the properties of the Zak transformation to derive a relation between matrix elements with respect to coherent states in and L 2(S 1). This provides an alternative way for computing semiclassical matrix elements for coherent states on the circle. In certain aspects, this method simplifies the semiclassical computations in particular if one is only interested in the classical limit, that is the zeroth order term in the semiclassical expansion.

An inverse problem for semilinear equations involving the fractional Laplacian

Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of the fractional Dirichlet-to-Neumann type map combined with the Runge approximation and the unique continuation property of the fractional Laplacian.

Final sheet thickness variation during the non-isothermal calendering process of rheological Prandtl fluid polymer

Industries widely use the calendering process to create coated fabrics, thermoplastic films, plastic sheeting, and textile fabrics to procure the prerequisite surface smoothness plus texture. This article inspects the non-isothermal calendering phenomena with heat transfer mechanism to report the rheological behavior of Prandtl fluid on the sensitivity of sheet thickness with velocity slip at roll’s surface. Lubrication theory is utilized to simplify the governing expressions before normalization. We obtained the zeroth plus first order perturbative solutions for the velocity profile, pressure gradient, pressure distribution, temperature, and sheet thickness. And other mechanical properties are evaluated with a numerical solution. Through graphs and tabular data, how material parameters influence the various flow and engineering parameters are reported. As it can be seen, the material parameters are the main parameters that control the pressure gradient, leading to different final sheet thickness and separating force. As the material parameters increased, sheet thickness and separating force increased.

Analytic solution of a fractional order mathematical model for tumour with polyclonality and cell mutation

It is well established that gliomas are heterogeneous (polyclonal), that the degree of heterogeneity always rises with grade. It is believed that the more cancerous cells have a greater propensity to mutate, increasing heterogeneity. Consequently, it is anticipated that a tumour will have a variety of cell types. In this work, a fractional diffusion model for tumour growth where two cell populations are assumed, which could have different diffusivity and proliferation rates, is studied and analysed. The coupled system is solved analytically via the zeroth order finite Hankel transform employing the fractional derivatives with exponential and Mittag-Leffler kernels, respectively and the obtained solutions simulated using MATLAB. Important highlights of the simulations include: (i.) using the Caputo fractional derivative, and considering the scenario when the rate of loss of cell population u(r,t) is α=0.5, keeping the other values of the parameters ν=1.2,β=0.1, it is observed that, near the centre of the tumour where biopsy is to be carried out, the tumour cell concentrations u(r,t) dominates v(r,t) when t=0.5 while tumour cell population v(r,t) dominates u(r,t) at time t=2.0; (ii.) with the Atangana–Baleanu derivative, and considering the same scenario it is observed that, near the centre of the tumour, the cell concentration v(r,t) dominates u(r,t) when t=0.5 while the dominance is much higher at time t=2.0. Thus, it is concluded that, the nature of kernel in the fractional operator could indeed alter the dominance between the tumour cell concentrations.

Electromagnetically induced grating realization in phaseonium

We propose a method to implement electromagnetically induced grating in a phaseonium medium that has been coherently generated via atomic mechanisms. Phaseonium atoms have a Λ-type structure and three distinct energy levels; such atoms are originally generated in a coherent superposition of two lower levels. The phaseonium system is comprised of three-level atoms with a Λ-type configuration, which are initially prepared in a coherent superposition of two lower levels. To accomplish this spatial modulation based on the susceptibility of phaseonium medium, a standing-wave field is used. By looking at how an optical field diffracts at different relative phases, we find that the zeroth and first order diffraction intensities increase as the relative phase changes. We also investigate the impact of the Rabi frequency of the field on diffraction intensity and notice that an increasing strength of the Rabi frequency leads to amplification in the intensity of both central zeroth order and first-order diffraction. Furthermore, it has been observed that a significant rise in diffraction intensity occurs at longer interaction lengths between external fields and the atomic medium.

Kinetic study of glycerol hydrodeoxygenation on Al2O3 and NiMo2C/Al2O3 catalysts

A kinetic study of glycerol hydrodeoxygenation (HDO) on NiMo2C/Al2O3 and Al2O3, prepared by sol-gel technique, was carried out in a batch reactor, from 250 °C to 285 °C, at high glycerol concentration (95wt%). Structural and surface properties of the catalysts were determined by XRD, nitrogen physisorption, TEM and NH3-TPD. Impregnation of alumina with Ni and Mo and subsequent carburization at 730 °C increased crystallite sizes and reduced total acidity of the catalyst to 1/3 that of pure alumina. All reactions were well fitted to a zeroth order model. Estimation of reagents mass transport rates suggests no diffusion limitation. Main products were propanediols, ethylene glycol and long-chain molecules from oligomerization reactions, as well as methane, ethane and propane. At this temperature range, long-chain compounds have the highest yields, mainly on alumina.

Carbon-Fiber- and Nanodiamond-Reinforced PLA Hierarchical 3D-Printed Core Sandwich Structures

The aim of the present paper is to investigate the mechanical behavior of FFF 3D-printed specimens of polylactic acid (PLA), PLA reinforced with nanodiamonds (PLA/uDiamond) and PLA reinforced with carbon fibers (PLA/CF) under various experimental tests such as compressive and cyclic compressive tests, nanoindentation tests, as well as scanning electron microscopy tests (SEM). Furthermore, the current work aims to design and fabricate hierarchical honeycombs of the zeroth, first and second order using materials under investigation, and perform examination tests of their dynamic behavior. The mechanical behavior of hierarchical sandwich structures was determined by conducting experimental bending tests along with finite element analysis (FEA) simulations. The results reveal that the incorporation of nanodiamonds into the PLA matrix enhanced the elastic modulus, strength and hardness of the 3D-printed specimens. In addition, the second order of the PLA/uD hierarchical sandwich structure presented increased strength, elastic and flexural modulus in comparison with the zeroth and first hierarchies. Regarding the dynamic behavior, the second order of the PLA/uD honeycomb structure revealed the biggest increase in stiffness as compared to PLA nanocomposite filaments.

Hessian-Aided Random Perturbation (HARP) Using Noisy Zeroth-Order Oracles.

In stochastic optimization problems where only noisy zeroth-order (ZO) oracles are available, the Kiefer-Wolfowitz algorithm and its randomized counterparts are widely used as gradient estimators. Existing algorithms generate the random perturbations from certain distributions with a zero mean and an isotropic (either identity or scalar) covariance matrix. In contrast, this work considers the generalization where the perturbations may have an anisotropic covariance based on the ZO oracle history. We propose to feed the second-order approximation into the covariance matrix of the random perturbation, so it is dubbed as Hessian-aided random perturbation (HARP). HARP collects two or more (depending on the specific estimator form) ZO oracle calls per iteration to construct the gradient and the Hessian estimators. We prove HARP's almost-surely convergence and derive its convergence rate under standard assumptions. We demonstrate, with theoretical guarantees and numerical experiments, that HARP is less sensitive to ill-conditioning and more query-efficient than other gradient approximation schemes whose random perturbations have an isotropic covariance.

Reactivity Differences of Trigonal Pyramidal Nonheme Iron(IV)-Oxo and Iron(III)-Oxo Complexes: Experiment and Theory.

High-valent metal-oxo species play critical roles in enzymatic catalysis yet their properties are still poorly understood. In this work we report a combined experimental and computational study into biomimetic iron(IV)-oxo and iron(III)-oxo complexes with tight second-coordination sphere environments that restrict substrate access. The work shows that the second-coordination sphere slows the hydrogen atom abstraction step from toluene dramatically and the kinetics is zeroth order in substrate. However, the iron(II)-hydroxo that is formed has a low reduction potential and hence cannot do OH rebound favorably. The tolyl radical in solution then reacts further with alternative reaction partners. By contrast, the iron(IV)-oxo species reacts predominantly through OH rebound to form alcohol products. Our studies show that the oxidation state of the metal influences reactivities and selectivities with substrate dramatically and that enzymes will likely need an iron(IV) center to catalyze C-H hydroxylation reactions.

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom.

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron-positron pairs), which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.

Directivity of quasi-SH0 modes in cubic anisotropic media

We studied the zeroth order shear horizontal modes (SH0 modes) and the quasi-SH0 modes in cubic-anisotropic plates and proposed a formula to describe the scattering directivity of these guided wave modes in arbitrary directions. The quasi-SH0 waves has many unique advantages. However, their velocity and amplitude are influenced by the material anisotropy and change with incidence orientation. In our finding, when the guided wave incidence orientation coincides with the material symmetry plane, the quasi-SH0 modes’ amplitudes generated by a uniform force are approximately equal. Otherwise, the amplitudes are significantly smaller. The formula derived by reciprocity consideration explains this phenomenon. We applied the formula to monocrystalline silicon. The results also show that the quasi-SH0 mode is both velocity non-dispersive and directivity non-dispersive in low-fd (frequency thickness product) state. We established an experimental system based on EMATs and verified the theoretical predictions. This paper completes the theoretical basis for damage reconstruction and acoustic imaging by guided waves in complex structures with cubic anisotropy.

SBMLKinetics: a tool for annotation-independent classification of reaction kinetics for SBML models

BackgroundReaction networks are widely used as mechanistic models in systems biology to reveal principles of biological systems. Reactions are governed by kinetic laws that describe reaction rates. Selecting the appropriate kinetic laws is difficult for many modelers. There exist tools that attempt to find the correct kinetic laws based on annotations. Here, I developed annotation-independent technologies that assist modelers by focusing on finding kinetic laws commonly used for similar reactions.ResultsRecommending kinetic laws and other analyses of reaction networks can be viewed as a classification problem. Existing approaches to determining similar reactions rely heavily on having good annotations, a condition that is often unsatisfied in model repositories such as BioModels. I developed an annotation-independent approach to find similar reactions via reaction classifications. I proposed a two-dimensional kinetics classification scheme (2DK) that analyzed reactions along the dimensions of kinetics type (K type) and reaction type (R type). I identified approximately ten mutually exclusive K types, including zeroth order, mass action, Michaelis–Menten, Hill kinetics, and others. R types were organized by the number of distinct reactants and the number of distinct products in reactions. I constructed a tool, SBMLKinetics, that inputted a collection of SBML models and then calculated reaction classifications as the probability of each 2DK class. The effectiveness of 2DK was evaluated on BioModels, and the scheme classified over 95% of the reactions.Conclusions2DK had many applications. It provided a data-driven annotation-independent approach to recommending kinetic laws by using type common for the kind of models in combination with the R type of the reactions. Alternatively, 2DK could also be used to alert users that a kinetic law was unusual for the K type and R type. Last, 2DK provided a way to analyze groups of models to compare their kinetic laws. I applied 2DK to BioModels to compare the kinetics of signaling networks with the kinetics of metabolic networks and found significant differences in K type distributions.

On the Time Frequency Compactness of the Slepian Basis of Order Zero for Engineering Applications

Time and frequency concentrations of waveforms are often of interest in engineering applications. The Slepian basis of order zero is an index-limited (finite) vector that is known to be optimally concentrated in the frequency domain. This paper proposes a method of mapping the index-limited Slepian basis to a discrete-time vector, hence obtaining a time-limited, discrete-time Slepian basis that is optimally concentrated in frequency. The main result of this note is to demonstrate that the (discrete-time) Slepian basis achieves minimum time-bandwidth compactness under certain conditions. We distinguish between the characteristic (effective) time/bandwidth of the Slepians and their defining time/bandwidth (the time and bandwidth parameters used to generate the Slepian basis). Using two different definitions of effective time and bandwidth of a signal, we show that when the defining time-bandwidth product of the Slepian basis increases, its effective time-bandwidth product tends to a minimum value. This implies that not only are the zeroth order Slepian bases known to be optimally time-limited and band-concentrated basis vectors, but also as their defining time-bandwidth products increase, their effective time-bandwidth properties approach the known minimum compactness allowed by the uncertainty principle. Conclusions are also drawn about the smallest defining time-bandwidth parameters to reach the minimum possible compactness. These conclusions give guidance for applications where the time-bandwidth product is free to be selected and hence may be selected to achieve minimum compactness.

Synthesis, and control release properties of Zirconium –AA7075 - beta naphtha oxy acetate nanocomposites

In this research, Beta naphtha oxy acetate (BNOA) was used as the guest anion, and Zirconium-aluminum 7075 layered double hydroxide (Zr-AA7075-LDH) was employed as the inorganic host, to create an organic–inorganic nanohybrid nanocomposite using the co-precipitation process. At a BNOA concentration of 0.08 M and a Zr/AA7075, R = 2 M ratio, a stable nanohybrid nanocomposite was produced. The formation of a Zr-AA7075-BNOA nanocomposite, wherein the nitrate ion interlayer gap in layered double hydroxide grew from 8.8 to 19.6 Å, demonstrates the successful intercalation of Beta naphtha oxy acetate into these spaces. Moreover, it was discovered that the Brunauer-Emmett-Teller surface area for Zr-AA7075-LDH and Zr-AA7075-BNOA nanocomposites rose from 4.23 to 45.84 m2 g−1. The generated nanocomposite is a mesoporous material with a BJH mean pore diameter of199 Å. CHNS analysis of the sample revealed that the Zr-AA7075- Beta naphtha oxy acetate nanocomposite material is 37.4% (w/w) depend on the carbon content. Pseudo-second order kinetics took over after 200 min of BNOA deintercalation from the Zr-AA7075 lamella being driven by zeroth and first order kinetics. It appears that the organic acid herbicide BNOA can be manufactured using layered double hydroxide as a carrier, as shown by the study's findings.

An Adversarial Attack Analysis on Malicious Advertisement URL Detection Framework

Malicious advertisement URLs pose a security risk since they are the source of cyber-attacks, and the need to address this issue is growing in both industry and academia. Several attempts have been made in recent years for malicious URL detection using machine learning (ML). The most widely used techniques extract linguistic features of URL string to extract features like bag-of-words (BoW) before applying ML model. Existing malicious URL detection techniques require effective manual feature engineering that can handle unseen features and generalise to test data. In this study, we extract a novel set of lexical and web-scrapped features and employ ML techniques for fraudulent advertisement URL detection. The combination set of six different kinds of features precisely overcomes the obfuscation in fraudulent URL classification. Based on distinct statistical properties, we use twelve differently formatted datasets for detection, prediction and classification task. We extend our prediction analysis for mismatched and unlabelled datasets. For this framework, we analyze the performance of four ML techniques: Random Forest, Gradient Boost, XGBoost and AdaBoost in the detection part. With our proposed method, we achieve a false negative rate up to 0.0037 while maintaining high detection accuracy of 99.63%. Moreover, we employ an unsupervised learning technique for data clustering using the K-Means algorithm for the visual analysis. This paper analyses the vulnerability of decision tree-based models using the limited knowledge attack scenario. We considered the exploratory attack during the test phase and implemented Zeroth Order Optimization adversarial attack on the detection models.

Non-dissipative electrically driven fluids

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid’s chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.

Minimizing a Low-Dimensional Convex Function Over a High-Dimensional Cube

For a matrix , , and a convex function , we are interested in minimizing over the set . We will study separable convex functions and sharp convex functions . Moreover, the matrix is unknown to us. Only the number of rows and are revealed. The composite function is presented by a zeroth and first order oracle only. Our main result is a proximity theorem that ensures that an integral minimum and a continuous minimum for separable convex and sharp convex functions are always “close” by. This will be a key ingredient in developing an algorithm for detecting an integer minimum that achieves a running time of roughly . In the special case when is given explicitly and is separable convex one can also adapt an algorithm of Hochbaum and Shanthikumar [J. ACM, 37 (1990), pp. 843–862]. The running time of this adapted algorithm matches the running time of our general algorithm.