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The cure progression of one-part room temperature vulcanizing (1-RTV) sealants and adhesives is a vital intrinsic material property for their typical end-use applications. Under-standing the key factors controlling the cure mechanism becomes more and more important given an ever-increasing demand to improve productivity by allowing assemblies using these materials to move faster through the manufacturing process. For 1-RTV systems, ultimate mechanical and adhesive strengths attain an equilibrium value as their cure proceeds in the presence of atmospheric moisture. A diffusion-controlled, moisture-cure mechanism was established for this family of materials about 10 years ago, most definitively by Comyn et al. The depth z of unidirectional cure with time t was derived to be a function of the vapor pressure p of water in the atmosphere in the proximity of the material surface, and two material properties: the permeability P of moisture through the cured layer and the equivalent material volume V reacting with 1 mol of water, and cure time, t, i.e. z=(2VPp t)1/2. Hence, the thickness of the cured layer should increase as t1/2. That is, a plot of z vs. t1/2 should yield a straight line where, for a particular RTV material, the mag-nitude of its slope is a function of the temperature and relative humidity (RH) during cure. This was shown for organic hot-melt adhesives and silicone sealants; validation of the moisture-cure model was demonstrated using gravimetrically based measurements to deter-mine V and P separately. However, a deviation from the moisture-cure model was reported from a study using an alkoxy silicone sealant in geometries requiring deep-section cure and, therefore, longer cure times. An increase in the slope of the z vs. t1/2 plot was observed after a certain time x interval that was a function of cure conditions. The change in cure rate was attributed to the migration of low molar mass crosslinkers and adhesion promoters towards the cure front and the eventual depletion of these species, which com-pete with the silicone polymer for reacting with the diffusing water. It was possible to determine the diffusion coefficient, D, of additives that act as adhesion promoters and crosslinkers in uncured alkoxy silicone sealant. From these studies, the utility of the moisture-cure diffusion model was demonstrated. The variables impacting cure performance are reviewed; and, a generalized form of the model is presented to account for variability in cure rates observed over extended time intervals in assembly geometries requiring deep-section cure. By plotting z as a function of (tp)1/2, data-sets for each material collected at different conditions of temperature and RH merged into a single straight line with a very high coefficient of determination. For end-users of 1-RTV silicone sealants and adhesives, this latter approach provides a material-specific reference line that demonstrates the corre-spondence between cure time and vapor pressure; i.e. a certain cured depth can be reached at short cure times with a high RH or at long times with a low RH. [ABSTRACT FROM AUTHOR]

In magnetic resonance imaging (MRI), high-power gradient power amplifiers (GPAs) are required to drive the gradient coils to generate strong and high-fidelity gradient fields. High precision is an essential requirement for the GPAs since precision directly impacts MRI imaging quality. Various aspects of the GPA have been the subject of research in the past years; however, high-precision GPA control that meets the stringent requirements of MRI applications is still a challenge. This article proposes a novel multi-rational-delay variables state space control method and an efficient out-of-band signal injection method to achieve GPA control accuracy at the level of one part per million at MVA output power levels. First, a systematic modeling and design method of the state space controller for high-power GPA is introduced utilizing state vectors with multi-rational-delay variables. This method improves the GPA dynamic performance significantly. Second, an efficient out-of-band signal injection method is presented to further improve the control precision at low output current, enabling the fulfillment of the challenging high-precision MRI requirements over the full GPA output range. Finally, the high-precision control method is validated in a GPA demonstrator with 500 A/1000 V output. Key results are a 30% improvement in current pulse reproducibility with respect to the conventional control method and a factor of 2.5 less noise at low currents. These experimental results validate the proposed novel method for the high-precision control of GPAs in MRI applications and prove its capability to contribute to significantly improved MRI image quality. [ABSTRACT FROM AUTHOR]

Objective: A major issue facing all health systems is improving population health while at the same time responding to both growing patient numbers and needs and developing and retaining the health care workforce. One policy response to workforce shortages has been the development of advanced clinical practice roles. In the context of an English national policy promoting such roles in the health service, we explored senior managers' and senior clinicians' perceptions of factors at the organization level that support or inhibit the introduction of advanced clinical practice roles. The investigation was framed by theories of the diffusion of innovation and the system of professions. Methods: We conducted a qualitative interview study of 39 senior manager and clinicians in 19 National Health Service acute, community, mental health and ambulance organizations across a metropolitan area in 2019. Results: Small numbers of advanced clinical practice roles were reported, often in single services. Four main influences were identified in the development of advanced clinical practice roles: staff shortages (particularly of doctors in training grades) combined with rising patient demand, the desire to retain individual experienced staff, external commissioners or purchasers of services looking to shape services in line with national policy, and commissioner-funded new roles in new ambulatory care services and primary care. Three factors were reported as enabling the roles: finance for substantive posts, evidence of value of the posts, and structural support within the organization. Three factors were perceived as inhibiting developing the roles: confusion and lack of knowledge amongst clinicians and managers, the availability of finance for the roles, and a nervousness (sometimes resistance) to introducing the new roles. Conclusions: While the national policy was to promote advanced clinical practice roles, the evidence suggested there was and would continue to be limited implementation at the operational level. Development scenarios that introduced new monies for such roles reduced some of the inhibiting factors. However, where the introduction of roles required funding to move from one part of a service to another, and potentially from one staff group to another, the growth of these roles was and is likely to be contested. In such scenarios, research and business evidence of relative advantage will be important, as too will be supporters in powerful positions. The paucity of publicly available evidence on the effectiveness of advanced clinical practice roles across the specialties and professions in different contexts requires urgent attention. [ABSTRACT FROM AUTHOR]

Iterative ensemble smoothers have been widely used for calibrating simulators of various physical systems due to the relatively low computational cost and the parallel nature of the algorithm. However, iterative ensemble smoothers have been designed for perfect models under the main assumption that the specified physical models and subsequent discretized mathematical models have the capability to model the reality accurately. While significant efforts are usually made to ensure the accuracy of the mathematical model, it is widely known that the physical models are only an approximation of reality. These approximations commonly introduce some type of model error which is generally unknown and when the models are calibrated, the effects of the model errors could be smeared by adjusting the model parameters to match historical observations. This results in a bias estimated parameters and as a consequence might result in predictions with questionable quality. In this paper, we formulate a flexible iterative ensemble smoother, which can be used to calibrate imperfect models where model errors cannot be neglected. We base our method on the ensemble smoother with multiple data assimilation (ES-MDA) as it is one of the most widely used iterative ensemble smoothing techniques. In the proposed algorithm, the residual (data mismatch) is split into two parts. One part is used to derive the parameter update and the second part is used to represent the model error. The proposed method is quite general and relaxes many of the assumptions commonly introduced in the literature. We observe that the proposed algorithm has the capability to reduce the effect of model bias by capturing the unknown model errors, thus improving the quality of the estimated parameters and prediction capacity of imperfect physical models. [ABSTRACT FROM AUTHOR]

We present an analytical model to predict the magnetoelectric (ME) effect in multiferroic laminated plates consisting of piezoelectric material and giant magnetostrictive material (GMM). The nonlinear behavior of GMM is taken into account by employing a simple quadratic constitutive relation. Both static and dynamic cases are considered. It is found that: (1) the dependence of ME effect on the applied magnetic field is quite different from that reported in the previous analysis; and (2) one part of the induced electric field has a frequency that is double the driving frequency of the applied magnetic field. The results indicate that multiferroic laminated plates with GMM layers have potential applications in multipliers and energy harvesters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a new coupled mathematical model of angiogenesis (new blood vessel growth) and tumor growth to study cancer development and anti-angiogenesis therapy. The angiogenesis part assumes the capillary to be a viscoelastic continuum whose stress depends on cell proliferation or death, and the tumor part is a Darcy’s law model regarding the tumor mass as an incompressible fluid where the nutrient-dependent growth elicits volume change. For the coupled model, we provide both an inviscid analysis and a parameter sensitivity analysis of the angiogenesis model in response to a stationary hypoxic tumor, and a steady state analysis of the tumor growth in response to a fixed and long blood capillary. The analysis shows that the stable steady state tumor with an invading blood capillary exists if and only if the nutrient release rate divided by the decay rate is less than the tumor viable limit, and the full tumor encloses one part of the capillary in this steady state. Afterwards, we use the coupled model to simulate vascularized tumor growth and anti-angiogenesis therapy. The simulations show that the tumor tends to maximize the nutrient transfer by blood vessel co-option and the anti-angiogenesis treatment by using growth factor neutralizing antibodies would regress the neovasculature and shrink the tumor size. However, the shrunken tumor mass could survive by feeding on mature blood vessels that resist the treatment. This implies the limited efficacy of the anti-angiogenesis monotherapy and its effect on vessel normalization. [ABSTRACT FROM AUTHOR]

Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of n is an ordered pair of partitions (π1; π2) with the sum of all of the parts being n. In this paper, we investigate arithmetic properties of bipartitions with designated summands. Let PD-2(n) denote the number of bipartitions of n with designated summands. We establish several Ramanujan-like congruences and an infinite family of congruences modulo 9 satisfied by PD-2(n). [ABSTRACT FROM AUTHOR]

This paper presents a new study based on a machine learning technique, specifically an artificial neural network, for predicting systolic blood pressure through the correlation of variables (age, BMI, exercise level, alcohol consumption level, smoking status, stress level, and salt intake level). The study was carried out using a database containing a variety of variables/factors. Each database of raw data was split into two parts: one part for training the neural network and the remaining part for testing the performance of the network. Two neural network algorithms, back-propagation and radial basis function, were used to construct and validate the prediction system. According to the experiment, the accuracy of our predictions of systolic blood pressure values exceeded 90%. Our experimental results show that artificial neural networks are suitable for modeling and predicting systolic blood pressure. This new method of predicting systolic blood pressure helps to give an early warning to adults, who may not get regular blood pressure measurements that their blood pressure might be at an unhealthy level. Also, because an isolated measurement of blood pressure is not always very accurate due to daily fluctuations, our predictor can provide the predicted value as another figure for medical staff to refer to. [ABSTRACT FROM AUTHOR]

The effect of the scale used to compute the interfacial curvature on the prediction of dynamic gas–liquid interfaces is investigated. A new interface curvature calculation methodology referred to herein as the Adjustable Curvature Evaluation Scale (ACES) is proposed. ACES leverages a weighted least squares regression to fit a polynomial through points computed on the volume-of-fluid representation of the gas–liquid interface. The interface curvature is evaluated from this polynomial. Varying the least squares weight with distance from the location where the curvature is being computed, adjusts the scale the curvature is evaluated on. ACES is verified using canonical static test cases and compared against second- and fourth-order height function methods. Simulations of dynamic interfaces, including a standing wave and oscillating droplet, are performed to assess the impact of the curvature evaluation scale for predicting interface motions. ACES and the height function methods are combined with two different unsplit geometric volume-of-fluid (VoF) schemes that define the interface on meshes with different levels of refinement. We find that the results depend significantly on curvature evaluation scale. Particularly, the ACES scheme with a properly chosen weight function is accurate, but fails when the scale is too small or large. Surprisingly, the second-order height function method is more accurate than the fourth-order variant for the dynamic tests even though the fourth-order method performs better for static interfaces. Comparing the curvature evaluation scale of the second- and fourth-order height function methods, we find the second-order method is closer to the optimum scale identified with ACES. This result suggests that the curvature scale is driving the accuracy of the dynamics. This work highlights the importance of studying numerical methods with realistic (dynamic) test cases and that the interactions of the various discretizations is as important as the accuracy of one part of the discretization. [ABSTRACT FROM AUTHOR]

Direct synthesis of dimethyl ether (DME) from syngas, was investigated over a CuO-ZnO-Al 2 O 3 catalyst for methanol synthesis and a γ-Al 2 O 3 catalyst for a methanol dehydration. On the base of mathematical modeling, thermodynamic analysis was carried out in a wide range of pressures (10–100 bar) and temperatures (220–280 °C) for binary mixtures (H 2 + CO) with an H 2 /CO = 1–6 M ratio. The influence of reaction conditions on the equilibrium content of components in the mixture was modelled. The effect of the loading method of catalysts of the methanol synthesis and its dehydration (layerwise loading, mixing) in the DME synthesis in a single reaction step on the CO conversion and the yield of DME was experimentally studied. It has been demonstrated that the layerwise combined loading with the intermediate mixed layer of CuO-ZnO-Al 2 O 3 catalysts of the methanol synthesis and the γ-Al 2 O 3 catalyst for the DME synthesis (2:1:2, ratio parts, i.e. two parts of the catalyst of the methanol synthesis, one part of a mixture of the catalysts and two parts of the catalyst of the methanol dehydration) allow to obtain the higher yield of DME. The effect of operating conditions (pressure, temperature, ratio H 2 /CO, time on stream, and catalyst stability) on the CO conversion and yield of DME was studied. The optimal conditions for loading variant 2:1:2 are: the pressure is 30 bar, the temperature is 280 °C and the initial ratio of H 2 /CO is equal to 2. At that, the CO conversion remains practically constant during 180 h reaction run. [ABSTRACT FROM AUTHOR]

A tunable frequency-doubled optoelectronic oscillator (FD-OEO) scheme based on a phase modulator (PM) located in a Sagnac loop is proposed and experimentally demonstrated. A light wave is halved and sent to the Sagnac loop along the clockwise (CK) and counter-clockwise (CCK) directions. The light wave along the CK direction is effectively modulated in the PM, while the one along the CCK direction is not modulated due to velocity mismatch. The optical output from the Sagnac loop is separated into two parts. One part is fed back to the radio-frequency (RF) port of the PM to form an OEO loop and obtain a fundamental signal. The other part is used to obtain a frequency-doubled signal by suppressing the optical carrier. The fundamental frequency of the OEO is continuously adjustable within the range from 3 to 20 GHz using a tunable electric filter, so a frequency-doubled signal with a frequency ranging from 6 to 40 GHz can be obtained. The phase noise performance of the generated fundamental and frequency-doubled signal is also studied. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a model for determining ordering/trade-credit policy of a supply chain, where one supplier sells a product to a retailer, who faces a deterministic demand, and may offer the retailer two types of trade credit contracts: a “one-part” or a “two-part” contract. We discuss the existence of the optimal solution to the model, and provide a simple algorithm for finding the optimal ordering and trade credit policy of two members. We specify the conditions under which it is beneficial in reducing operational cost for the supplier to offer the two trade credit contracts. Through numerical experiments, we reveal that it is more superior in reducing operational cost for the supplier to offer a two-part credit than to offer a one-part credit, which can be extended to a multi-part credit. The sensitivity analysis is presented at the end of the paper. [Copyright &y& Elsevier]

Abstract: For decades, the main ways to study the effect of one part of the nervous system upon another have been either to stimulate or lesion the first part and investigate the outcome in the second. This article describes a fundamentally different approach to identifying causal connectivity in neuroscience: a focus on the predictability of ongoing activity in one part from that in another. This approach was made possible by a new method that comes from the pioneering work of Wiener (1956) and Granger (1969). The Wiener–Granger method, unlike stimulation and ablation, does not require direct intervention in the nervous system. Rather, it relies on the estimation of causal statistical influences between simultaneously recorded neural time series data, either in the absence of identifiable behavioral events or in the context of task performance. Causality in the Wiener–Granger sense is based on the statistical predictability of one time series that derives from knowledge of one or more others. This article defines Wiener–Granger Causality, discusses its merits and limitations in neuroscience, and outlines recent developments in its implementation. [Copyright &y& Elsevier]

A basis of Hermite splines is used in conjunction with the collocation method to solve the orbital equations for diatomic molecules. Accurate solutions of the Hartree-Fock equations are obtained using iterative methods over most regions of space, while solving the equations by Gaussian elimination near the nuclear centres. In order to improve the speed and accuracy of our iterative scheme, a new self-adjoint form of the Hartree-Fock equation is derived. Using this new equation, our iterative subroutines solve the Hartree-Fock equations to one part in 10[sup 6]. The Gaussian elimination routines are accurate to better than one part in 10[sup 8]. [ABSTRACT FROM AUTHOR]

We study a trilinear singular integral form acting on twodimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the motivation for introducing it lies in its large symmetry groups acting on the Fourier side. Another part of the motivation is that this form stands between the bilinear Hilbert transforms and the first Calderón commutator, in the sense that it can be reduced to a superposition of the former, while it also successfully encodes the latter. As the main result we determine the exact range of exponents in which the Lp estimates hold for the considered form. [ABSTRACT FROM AUTHOR]

In the current research papers on multi-agent (multi-person) scheduling, a person's objective function is always considered as a cost function on scheduling, whereas a cooperative profit function is defined to serve as his objective one in this paper. In the two-person scheduling problem addressed in this paper, the two persons jointly order a common operational time interval of a single machine. Each person needs to process a set of his own jobs in that time window. The same objective function of each person still relies on the sequence of all the jobs of both persons since each part of the function is determined by some given parameters except one part assumed to be a given multiple of the total completion time of his own jobs. The two persons have to negotiate a job sequence and determine the (related) final solution on cooperative profit allocation. Such a two-person scheduling problem is essentially a cooperative game. An algorithm is designed to yield the cooperative-profit-based Pareto efficient solution set acting as the first game-based solution concept in this paper. The parallelized version of the algorithm is also developed. The second game-based solution concept is the Shapley value appropriate for the above cooperative-game situation on two-person scheduling. Several instances are presented and analyzed to reveal the necessity to employ the two solution concepts together. [ABSTRACT FROM AUTHOR]

We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies. Additionally, frustration parameters for the interactions of the cross-network phases are introduced. This may be regarded as a model of competing populations: internal to any one network phase synchronisation is a target state, while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor. We conduct fixed point analyses for two regimes: one, where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other; the second where one part of a population remains fixed in phase in relation to the other population, but where instability may occur within the first population leading to ‘fragmentation’. We compare analytic results to numerical solutions for the system at various critical thresholds. [ABSTRACT FROM AUTHOR]

The authors propose a mathematical model for a multi-channel queueing system with feedback in which one part of calls instantaneously enters the system for repeated service and the other part either retries in some random time or finally leaves the system. The behavior of the serviced calls is randomized. Both exact and asymptotic methods are developed to calculate the characteristics of the proposed model. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to discuss the characteristics of several stochastic simulation methods applied in computation issue of structure health monitoring (SHM). Design/methodology/approach – On the basis of the previous studies, this research focusses on four promising methods: transitional Markov chain Monte Carlo (TMCMC), slice sampling, slice-Metropolis-Hasting (M-H), and TMCMC-slice algorithm. The slice-M-H is the improved slice sampling algorithm, and the TMCMC-slice is the improved TMCMC algorithm. The performances of the parameters samples generated by these four algorithms are evaluated using two examples: one is the numerical example of a cantilever plate; another is the plate experiment simulating one part of the mechanical structure. Findings – Both the numerical example and experiment show that, identification accuracy of slice-M-H is higher than that of slice sampling; and the identification accuracy of TMCMC-slice is higher than that of TMCMC. In general, the identification accuracy of the methods based on slice (slice sampling and slice-M-H) is higher than that of the methods based on TMCMC (TMCMC and TMCMC-slice). Originality/value – The stochastic simulation methods evaluated in this paper are mainly two categories of representative methods: one introduces the intermediate probability density functions, and another one is the auxiliary variable approach. This paper provides important references about the stochastic simulation methods to solve the ill-conditioned computation issue, which is commonly encountered in SHM. [ABSTRACT FROM AUTHOR]

In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a scheduling problem for a two-stage production system including machining operations and assembly operations is studied. In this system, a number of products of different kinds are produced. Each product is assembled with a set of several parts. The first stage is a hybrid flow shop to produce parts. All machines can process all kinds of parts in this stage, but each machine can process only one part at a time. The second stage is a single assembly machine or a single assembly team of workers. The considered objective is to minimize the completion time of all products (makespan). A mathematical modeling is presented, and since this problem has been proved strongly nondeterministic polynomial-time hard, a series of heuristic algorithms based on the basic idea of Johnson algorithm is proposed. Also, two lower bounds is introduced and improved to evaluate the final solution obtained from heuristic algorithms. The numerical experiments are used to evaluate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Underwater high speed target counter-rotation propeller always works at cavitation condition, the cavitation noise line-spectrum is due to the interaction between fore and aft propeller, and the interaction between the fore or aft propeller and wake of the ship. According to the acoustic analogy equation of Goldstein and making vacuole as one part of propeller, the academic prediction of counter-rotation propeller cavitation line-spectrum frequency is presented. The far field sound pressure expression of monopole sound source is deduced, and the line-spectrum prediction frequency is gained. The counter-rotation propeller cavitation is numerically simulated using Schnerr-sauer cavitation model, RNG k-ε turbulence model and dynamic mesh model. The resuits shows that the predicted cavity shapes of DTMB4381 propeller agrees well with the experimental observation and numerical simulation result on open literature, and the counter-rotation propeller cavitation line-spectrum frequency is got by this method which agrees with the result of Academic prediction absolutely. [ABSTRACT FROM AUTHOR]

Abstract: The Dicke–Jaynes–Cummings–Gaudin model describes a collection of spins coupled to a harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each point in phase space the list of values of the conserved Hamiltonians. We identify all the critical points of this map and we compute the corresponding quadratic normal forms, using the Lax matrix representation of the model. The normal coordinates are constructed by a procedure which appears as a classical version of the Bethe Ansatz used to solve the quantum model. We show that only elliptic or focus–focus singularities are present in this model, which provides an interesting example of a symplectic toric action with singularities. To explore these, we study in detail the degeneracies of the spectral curves for the and cases. This gives a complete picture for the image of the momentum map (IMM) and the associated bifurcation diagram. For we found in particular some lines of rank 1 which lie, for one part, on the boundary of the IMM, where they behave like an edge separating two faces, and which go, for another part, inside the IMM. [Copyright &y& Elsevier]

This study examined the relationships among adolescents’ emotion regulation strategies (suppression and cognitive reappraisal), self-concept, and internalizing problems using structural equation modeling. The sample consisted of 438 early adolescents (13 to 15 years old) in Taiwan, including 215 boys and 223 girls. For both boys and girls, suppression was negatively associated, and cognitive reappraisal was positively associated with self-concept. Self-concept negatively predicted adolescents’ internalizing problems. The findings support the hypothesis that self-concept mediates the relationship between emotion regulation and internalizing problems. These findings support generalization of one part of Cicchetti’s and Toth’s model of the development of internalizing problems to an Asian culture. [ABSTRACT FROM AUTHOR]

Abstract: Microgrippers are amongst the preferred tools for microassembly applications and have drawn extensive attention of the researches on their mechanism and actuation principles. One of key parameters is efficiency of microgripping systems in handling more than one part at a time. Multi-part-gripping mechanism is one of the least investigated subjects in the published literature. In this paper, an electrostatic microgripping system using comb drive mechanism is designed with the capability of gripping two micro components simultaneously. S-type springs are utilized to amplify the displacement range of microgripper arms. The objects gripped with this microgripping system are diverse from biomedical (e.g. arrow shaped microshuttles); MEMS and microelectronic field with the dimensions from 145 to 100μm for the operating voltage of 20–80V. A mathematical model with derived formulas is developed showing displacement of the tool versus applied voltage. Estimation of the performance of comb-drive is done through considering five capacitors all around a comb finger. The designed model predicts the displacement of the rotor more accurately compared to dominant method of calculating the equivalent capacity of only two lateral capacitors. Furthermore a multi-field simulation of the electrostatic comb finger of the comb drive is performed using finite element method. The FEA results show good agreement with the prediction obtained from analytical model. Microgripper function is enhanced through introducing a suspension system with optimum stiffness values. It helps the microgripper work under lower levels of actuating voltage. Finally, to verify analytical results, the microgripper is fabricated and the displacements are measured that compare well with analytical results and numerical simulation. [Copyright &y& Elsevier]

Abstract: Based on the activated sludge model no.3 (ASM3), a new kinetic expression describing substrate removal and biomass growth mechanism occurring in activated sludge system under aerobic condition was established. The new model proposed that under feast condition, one part of substrate was utilized directly for biomass growth and the other part was stored as internal storage products and simultaneously the storage products were used for biomass growth. The model was successfully calibrated on oxygen uptake rate (OUR) data and off-line soluble chemical oxygen demand (COD) dynamic variations obtained from batch experiments with biomass from a full-scale wastewater treatment plant (WWTP). OUR predictions with the calibrated model could reasonably describe the OUR profile after pulse addition of acetate, i.e., the OUR transiently reached a very high level, and then increased gradually to a maximum level until the initial substrate was taken up for storage and biomass growth. This new model also, for the first time, highlighted the significant effect of the biomass storage products concentration before pulse addition of acetate on OUR profile. [Copyright &y& Elsevier]

Abstract: Cell movement is a complex process. Cells can move in response to a foreign stimulus in search of nutrients, to escape predation, and for other reasons. Mathematical modeling of cell movement is needed to aid in achieving a deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work we consider cell movement that can be separated into two parts: one part is in direct response to a stimulus and the other is due to uncertainties and other reasons for the movement. In order to deal with the deterministic and random aspects of cell movement, an individual based model is created to simulate cells moving in the presence of heterogeneously distributed stimulus molecules. The model is then upscaled, starting with an analysis of the transition probabilities of individuals at each site, to obtain a continuous partial differential equation model. Finally, the two models are numerically compared to each other for a variety of different parameter values. [Copyright &y& Elsevier]

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. [ABSTRACT FROM AUTHOR]

We prove a theorem on the asymptotic stability of power type with respect to one part of the phase variables and on the uniform boundedness of the solutions of a multiply connected system of differential equations with respect to the other part of the variables. [ABSTRACT FROM AUTHOR]

In many situations in physics, engineering and biology time delays arise naturally due to the time needed to transport information from one part of the system to another and/or to react to incoming information. When differential equations are used in the mathematical modelling, then incorporating time delays leads to a description by a delay differential equation. We consider here a class of second-order scalar delay equations without instantaneous feedback, where the delays enter according to a distribution function. This is a natural description whenever there is more than one delay. In this article we show that for this class of systems one can derive stability information about the distributed-delay system by considering the single-delay system where the delay is the mean delay of the distribution function. More specifically, we prove that the asymptotic stability of the zero solution of the second-order delay equation with symmetric delay distribution is implied by the stability of the associated mean-delay equation. Our proof is based on the comparison of stability charts of the two equations. [ABSTRACT FROM AUTHOR]

Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural systems. Understanding the time-varying relationship of emotion and cognition is a challenging goal with important implications for neuroscience. We formulate here the dynamical model of emotion-cognition interaction that is based on the following principles: (1) the temporal evolution of cognitive and emotion modes are captured by the incoming stimuli and competition within and among themselves (competition principle); (2) metastable states exist in the unified emotion-cognition phase space; and (3) the brain processes information with robust and reproducible transients through the sequence of metastable states. Such a model can take advantage of the often ignored temporal structure of the emotion-cognition interaction to provide a robust and generalizable method for understanding the relationship between brain activation and complex human behavior. The mathematical image of the robust and reproducible transient dynamics is a Stable Heteroclinic Sequence (SHS), and the Stable Heteroclinic Channels (SHCs). These have been hypothesized to be possible mechanisms that lead to the sequential transient behavior observed in networks. We investigate the modularity of SHCs, i.e., given a SHS and a SHC that is supported in one part of a network, we study conditions under which the SHC pertaining to the cognition will continue to function in the presence of interfering activity with other parts of the network, i.e., emotion. [ABSTRACT FROM AUTHOR]

Abstract: The interferon system provides a powerful and universal intracellular defense mechanism against viruses. As one part of their survival strategies, many viruses have evolved mechanisms to counteract the host type I interferon (IFN-α/β) responses. In this study, we attempt to investigate virus- and double-strand RNA (dsRNA)-triggered type I IFN signaling pathways and understand the inhibition of IFN-α/β induction by viral proteins using mathematical modeling and quantitative analysis. Based on available literature and our experimental data, we develop a mathematical model of virus- and dsRNA-triggered signaling pathways leading to type I IFN gene expression during the primary response, and use the genetic algorithm to optimize all rate constants in the model. The consistency between numerical simulation results and biological experimental data demonstrates that our model is reasonable. Further, we use the model to predict the following phenomena: (1) the dose-dependent inhibition by classical swine fever virus (CSFV) Npro or Erns protein is observed at a low dose and can reach a saturation above a certain dose, not an increase; (2) Erns and Npro have no synergic inhibitory effects on IFN-β induction; (3) the different characters in an important transcription factor, phosphorylated IRF3 (IRF3p), are exhibited because Npro or Erns counteracted dsRNA- and virus-triggered IFN-β induction by targeting the different molecules in the signaling pathways and (4) Npro inhibits the IFN-β expression not only by interacting with IFR3 but also by affecting its complex with MITA. Our approaches help to gain insight into system properties and rational therapy design, as well as to generate hypotheses for further research. [Copyright &y& Elsevier]

Abstract: In this paper we study the analyticity of solutions to a free boundary problem modeling the growth of multi-layer tumors. The problem consists of three elliptic equations defined on a strip-like domain in , with one part of the boundary moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation, with the surface tension effect taken into consideration. Due to the unknown boundary and surface tension effect, this problem is an essentially nonlinear problem. By following a functional analytical approach and the theory of maximal regularity, we prove that solutions of this free boundary problem are real analytic in time and space for any positive time, even if the given initial data admit mild regularity only. [Copyright &y& Elsevier]

In this paper we present a modeling framework for analyzing natural gas markets, taking into account the specific technological issues of gas transportation. We model the optimal dispatch of supply and demand in natural gas networks, with different objective functions, i.e., maximization of flow, and different economic surpluses. The models take into account the physical structure of the transportation networks, and examine the implications it has for economic analysis. More specifically, pressure constraints create system effects, and thus, changes in one part of the system may require significant changes elsewhere. The proposed network flow model for natural gas takes into account pressure drops and system effects when representing network flows. Pressure drops and pipeline flows are modeled by the Weymouth equation. A linearization of the Weymouth equation makes economic analyses computationally feasible even for large networks. However, in this paper, the importance of combining economics with a model for pressure drops and system effects is illustrated by small numerical examples. [ABSTRACT FROM AUTHOR]

We consider the formation of solid drops ("islands") occurring in the growth of strained solid films. Beginning from a detailed model for the growth of an alloy film that incorporates the coupling between composition, elastic stress and the morphology of the free boundary, we develop an asymptotic description of the shape and compositional nonuniformity of small alloy islands grown at small deposition rates. A key feature of the analysis is a "thin domain" scaling in the island which enables recasting the free boundary problem into a set of integrodifferential equations for the shape and composition profile. The integrodifferential system can be decomposed into two parts: one part gives a single integrodifferential equation for the shape analogous to that obtained for a single-component island determined by Shanahan and Spencer (2002), and the other part gives the composition profile in terms of the shape. Thus, the shape of an alloy island is identical to that of a single-component island with the same system parameters, but with a nonuniform composition that depends on the stress-composition coupling and alloy solution thermodynamics. Finally, we characterize the structure and magnitude of the compositional nonuniformity and also interpret our theoretical results in the context of SiGe alloy films. [ABSTRACT FROM AUTHOR]

In this paper, groups of individual features, i.e., a point, a line, and a plane, are called clusters and are used to constrain sufficiently the relative location of adjacent parts. A new mathematical model for representing size and geometric tolerances is applied to a point-line cluster of features that is used to align adjacent parts in two-dimensional space. First, tolerance-zones are described for the point-line cluster. A Tolerance-Map® (Patent no. 69638242), a hypothetical volume of points, is then established which is the range of a mapping from all possible locations for the features in the cluster. A picture frame assembly of four parts is used to illustrate the accumulations of manufacturing variations, and the T-Maps® provide stackup relations that can be used to allocate size and orientational tolerances. This model is one part of a bilevel model that we are developing for size and geometric tolerances. At the local level the model deals with the permitted variations in a tolerance zone, while at the global level it interrelates all the frames of reference on a part or assembly. [ABSTRACT FROM AUTHOR]

In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. [ABSTRACT FROM AUTHOR]

Abstract: Polynomial regression models are often used in practice although practitioners are seldom sure whether their assumed linear regression model is at least approximately true. Therefore, designs are most interesting in practice with which the linear model can be checked. Optimal designs for polynomial regression, however, have not this property. To get practically attractive designs, Bischoff and Miller [2003. Optimal designs efficient for lack of fit tests. Preprint.] have suggested the following strategy. One part of the design points are used to be able to carry out a lack of fit test with a good power for practically interesting alternatives. The rest of the design points are determined in such a way that the whole design is optimal for inference on the unknown parameter in case the lack of fit test does not reject the linear regression model. To solve this problem, efficient lack of fit designs were introduced in Bischoff and Miller [2003. Optimal designs efficient for lack of fit tests. Preprint.]. In this class of designs we explicitly determine -optimal designs for polynomial regression of degree in this paper. More exactly, for we determine all -optimal designs for polynomial regression of degree . For we determine the -optimal designs for polynomial regression of degree if we restrict ourselves to designs that deliver highly efficient lack of fit tests. [Copyright &y& Elsevier]

Two models are presented for the motion of a vortex near a gap in an infinitely long straight barrier: a problem of geophysical significance. The first model considers a line vortex for which the trajectories are obtained analytically and are generalized to include simple ambient flows. The criterion determining whether in the absence of background flow a vortex originating far from the gap passes through or leaps across the gap is derived. The second model considers a finite area patch of constant vorticity and is based on conformal mapping and the numerical method of contour surgery. The two models enable a comparison of the trajectories of line vortices and vortex patches. In most examples the centroid of the patch is constrained to follow closely the trajectory of a line vortex of the same circulation. An exception occurs when flow through the gap forces the vortex patch close to one of the edges of the barrier where it splits into two with only one part of the vortex passing through the gap. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a split-and-merge expectation-maximization (SMEM) algorithm to overcome the local maxima problem in parameter estimation of finite mixture models. In the case of mixture models, local maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations, we repeatedly perform simultaneous split-and-merge operations using a new criterion for efficiently selecting the split-and-merge candidates. We apply the proposed algorithm to the training of gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split-and-merge operations to improve the likelihood of both the training data and of held-out test data. We also show the practical usefulness of the proposed algorithm by applying it to image compression and pattern recognition problems. [ABSTRACT FROM AUTHOR]

The use of the Nernst–Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, i, via an equation expressing the potential gradient as an explicit function of i. The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the diffusion layer (including the electroneutral region and the extended space charge region, zone (I) with an analytical solution in the other part (the quasi-equilibrium electric double layer (EDL), zone (II). It is shown that this approach (called the "zonal" model) allows reducing the computational complexity of the problem tens of times without significant loss of accuracy. An additional simplification is introduced by neglecting the thickness of the quasi-equilibrium EDL in comparison to the diffusion layer thickness (the "simplified" model). For the first time, the distributions of concentrations, space charge density and current density along the distance to an ion-exchange membrane surface are computed as functions of time in galvanostatic mode. The calculation of the transition time, τ, for an ion-exchange membrane agree with an experiment from literature. It is suggested that rapid changes of space charge density, and current density with time and distance, could lead to lateral electroosmotic flows delaying depletion of near-surface solution and increasing τ. [ABSTRACT FROM AUTHOR]

In view of the complicated structure of the deflector–jet mechanism, a mathematical model based on the turbulent jet flow theory in the deflector–jet amplifier is proposed. Considering the energy transformation and momentum variation, an equation of the flow velocity distribution at the key fluid region is established to describe the morphological changes of the fluid when it passes through the deflector and jets into the receiver. Moreover, the process is segmented into four stages. According to the research results, the oil enters the deflector and impinges with the side wall. Then one part of the oil’s flow velocity decreases and a high pressure zone is formed by the oil accumulation, the other part of the oil reverses out of the deflector along the side wall. Prior to entering the receiver, the flow is a kind of plane impinging jet. Virtually, the working pressure of the receiver is generated by the impact force, while the high speed fluid flows out of the receiver and forms a violent vortex, which generates negative pressure and causes the oil to be gasified. Compared with the numerical simulation results, the turbulent jet model that can effectively describe the characteristics of the deflector–jet mechanism is accurate. In addition, the calculation results of the prestage pressure characteristic have been verified by experiments. [ABSTRACT FROM AUTHOR]