Applied Mathematics and Physics

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the
field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is
a three-dimensional phenomenon.

In this paper we have tried to describe a gauge group for gravitational potential associated with the elementary particle as described by their spiral structure in accordance with the standard model. It relates to the framework of quantum field theory considering the Dark Potential Waves which constitutes the Universe to be destructively interfering through Symmetry which breaks spontaneously through autocatalysis to initiate the Higgs Mechanism which consecutively defines the gravitational potential resulting in various spiral forms of particles. It also redefines the formation of Spiral Structure of Elementary Particles in context to formation of Sea Shells.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

During end of last May there was a news head line : 13 killed, 28 injured in four districts by lightning in West Bengal during heavy pre-monsoon rains which lashed the state. Among the killed five persons were in Murshidabad district, three in Purulia, two in Burdwan district and two in West Midnapore district. In Murshidabad, Five persons were killed in lightning in Hariharpur and Raghunathganj areas of Murshidabad district. Two persons were killed at Maheshpur village, one at Daltonpur village in Hariharpur area, while two others were killed at Rajanagar village in Raghunathganj, official sources said. Three others were also injured in lightning in Raghunathganj. A woman and two men were killed as lightning struck them in Jhalda, Baghmundi and Kashipur area of Purulia district while they were working in agricultural fields. A 48-year-old man was killed in Khandaghosh area when he was working in his field this morning, while a 23-year-old woman was killed when lightning struck the shed under which she had taken shelter during rain in Kumarpur. Another woman, who was accompanying her for collecting firewood, was seriously injured. Two sisters were killed in Gobindapur village under Ghatal area of West Midnapore district when lightning struck while they were returning home from a fair price shop. 24 people were injured in another incidence of lightning at Chandrakona area of West Midnapore district. They were waiting to join work allotted to them under MNREGA at Tolbostihala village when lightning struck them. Developing countries have long lists of problems—illiteracy, disease, hunger, corruption. There's one more problem that has gotten less attention, until recently: lightning strikes, which cause a disproportionately high number of deaths in developing countries.

The governing equation of transonic small disturbance flow presents a non-linear partial differentia equation whih is difficult to solve. The method of parametric differentiation reduces the non-linear partial differential equation of transonic flow into an ordinary differential equation with variable coefficient, which Is generally much simpler to solve. Further simplification is introduced, as is done in the method of local linearization, by assuming (1-M12) to vary sufficiently slowly, so that in some part of the analysis its derivative with respect to x can be disregarded. Based ipon these methods, the lifting transonic flow was analyzed. For the subsonic and supersonic parts, closed form solutions were obtained. For the case M1 1, the method yields an integral equation, which can be solved by an iterative scheme starting from the non-lifting solution.

Aim: Our work investigates the use of "external momentum" in the context of hypertrophy oriented training. This is momentum supplied to the load (such as a dumbbell) used in an exercise by means of action of muscles not inherently involved in the exercise. We challenge the general consensus that the use of such momentum often described as "cheating" is counterproductive.

Methods: We focus on the use of external momentum in the shoulder lateral raise and adopt a framework whereby exercise execution is simulated on a computer. This is achieved using a physical model of motion which is combined with anthropomorphic measurements and empirical data of muscular recruitment from previous work.

Results: The introduction of moderate momentum (producing initial angular velocities around 57.5 deg/s) increases the torque of the target muscles even without an increase in the load used. A moderate increase in the load and the use of momentum allows the torque to be increased even further. In contrast, excessive use of momentum results in lower demands on the target muscles, while an excessive increase of the load reduces the total hypertrophy stimulus by virtue of the decreased number of repetitions which can be performed successfully and thus the dramatically shortened time under tension.

Conclusion: Our results disprove the conventional belief that the use of external momentum necessarily reduces the overload of the target muscles. A moderate use of external momentum increases both the per-repetition peak torque and the total hypertrophy stimulus in a set.

This work is motivated by two important trends in consumer computing: (i) the growing pervasiveness of mobile computing devices, and (ii) the users' desire for increasingly complex but readily acquired and manipulated information content. Specifically, we develop and describe a system for 3D model creation of an object, using only a standard mobile device such as a smart phone. Our approach applies the structured light projection methodology and exploits multiple image input such as frames from a video sequence. In comparison with previous work, a significant further challenge addressed here is that of lower quality input data and limited hardware (processing power and memory, camera and projector quality). Novelties include: (i) a comparison of projection pattern detection approaches in the context of a mobile environment - a robust method combining colour detection and a phase congruency descriptor is proposed, (ii) a model for single view reconstruction which exploits epipolar, coplanarity and topological constraints, (iii) the use of mobile device sensor data in the iterative closest point algorithm used to register multiple partial 3D reconstructions, and (iv) two heuristics for determining the order in which buffered single view based reconstructions are merged. Our experiments demonstrate that visually appealing results are obtained in a speedy manner which does not require specialist knowledge or expertise from the user.

Resonance-like phenomena in axisymmetric Poiseuille flows of viscoelastic fluids are studied. It is shown that instantaneous flow velocities of the upper convected Maxwell fluid with a spectrum of relaxation times drastically increase at certain frequencies of the oscillating pressure gradient. This effect becomes more pronounced as the tube radius gets smaller. Non-linear constitutive structures are also considered to show that the most effective mean flow rate enhancement for pulsating flows can be reached at the resonance frequencies.

Over the course of the last decade, infrared (IR) and particularly thermal IR imaging based face recognition has emerged as a promising complement to conventional, visible spectrum based approaches which continue to struggle when applied in the real world. While inherently insensitive to visible spectrum illumination changes, IR images introduce specific challenges of their own, most notably sensitivity to factors which affect facial heat emission patterns, e.g.\ emotional state, ambient temperature, and alcohol intake. In addition, facial expression and pose changes are more difficult to correct in IR images because they are less rich in high frequency detail which is an important cue for fitting any deformable model. In this paper we describe a novel method which addresses these major challenges. Specifically, to normalize for pose and facial expression changes we generate a synthetic frontal image of a face in a canonical, neutral facial expression from an image of the face in an arbitrary pose and facial expression. This is achieved by piecewise affine warping which follows active appearance model (AAM) fitting. This is the first publication which explores the use of an AAM on thermal IR images; we propose a pre-processing step which enhances detail in thermal images, making AAM convergence faster and more accurate. To overcome the problem of thermal IR image sensitivity to the exact pattern of facial temperature emissions we describe a representation based on reliable anatomical features. In contrast to previous approaches, our representation is not binary; rather, our method accounts for the reliability of the extracted features. This makes the proposed representation much more robust both to pose and scale changes. The effectiveness of the proposed approach is demonstrated on the largest public database of thermal IR images of faces on which it achieved 100% identification rate, significantly outperforming previously described methods.

A large corpus of data obtained by means of empirical study of neuromuscular adaptation is currently of limited use to athletes and their coaches. One of the reasons lies in the unclear direct practical utility of many individual trials. This paper introduces a mathematical model of adaptation to resistance training, which derives its elements from physiological fundamentals on the one side, and empirical findings on the other. The key element of the proposed model is what is here termed the athlete's capability profile. This is a generalization of length and velocity dependent force production characteristics of individual muscles, to an exercise with arbitrary biomechanics. The capability profile - a two-dimensional function over the capability plane - plays the central role in the proposed model of the training-adaptation feedback loop. Together with a dynamic model of resistance the capability profile is used in the model's predictive stage when exercise performance is simulated using a numerical approximation of differential equations of motion. Simulation results are used to infer the adaptational stimulus, which manifests itself through a fed back modification of the capability profile. It is shown how empirical evidence of exercise specificity can be formulated mathematically and integrated in this framework. A detailed description of the proposed model is followed by examples of its application - new insights into the effects of accommodating loading for powerlifting are demonstrated. This is followed by a discussion of the limitations of the proposed model and an overview of avenues for future work.

Wireless sensor networks (WSNs) have attracted a wide range of disciplines where close interactions with the physical world are essential. The distributed sensing capabilities and the ease of deployment provided by a wireless communication paradigm make WSNs an important component of our daily lives. By providing distributed, real-time information from the physical world, WSNs extend the reach of current cyber infrastructures to the physical world. In this paper, we present a detailed explanation of wireless sensor networks architecture and protocol. Our aim is to provide a contemporary look at the current state of the art in WSNs and discuss the still-open research issues in this field.

In this paper we have tried to describe a gauge group for gravitational potential associated with the elementary particle as described by their spiral structure in accordance with the standard model. It relates to the framework of quantum field theory considering the Dark Potential Waves which constitutes the Universe to be destructively interfering through Symmetry which breaks spontaneously through autocatalysis to initiate the Higgs Mechanism which consecutively defines the gravitational potential resulting in various spiral forms of particles. It also redefines the formation of Spiral Structure of Elementary Particles in context to formation of Sea Shells.

I describe a simple modification which can be applied to any citation count-based index (e.g. Hirsch's h-index) quantifying a researcher's publication output. The key idea behind the proposed approach is that the merit for the citations of a paper should be distributed amongst its authors according to their relative contributions. In addition to producing inherently fairer metrics I show that the proposed modification has the potential to partially normalize for the unfair effects of honorary authorship and thus discourage this practice.

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of ob...

In this paper we are interested in analyzing behaviour in crowded public places at the level of holistic motion. Our aim is to learn, without user input, strong scene priors or labelled data, the scope of "normal behaviour" for a particular scene and thus alert to novelty in unseen footage. The first contribution is a low-level motion model based on what we term tracklet primitives, which are scene-specific elementary motions. We propose a clustering-based algorithm for tracklet estimation from local approximations to tracks of appearance features. This is followed by two methods for motion novelty inference from tracklet primitives: (a) an approach based on a non-hierarchial ensemble of Markov chains as a means of capturing behavioural characteristics at different scales, and (b) a more flexible alternative which exhibits a higher generalizing power by accounting for constraints introduced by intentionality and goal-oriented planning of human motion in a particular scene. Evaluated on a 2h long video of a busy city marketplace, both algorithms are shown to be successful at inferring unusual behaviour, the latter model achieving better performance for novelties at a larger spatial scale.

A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is, the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method takes into account the non-Gaussian outliers, and does not require the assumption of a priori error bounds as in other smoothing techniques which may lead to instability or to a stable solution not representative of the true solution. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from
experimental material functions. The relaxation spectra of some materials obtained via the proposed adaptive-robust minimax algorithm and experiments run in a rotary viscometer are presented.

In this paper, we determine the number of zeros and the zero inclusion regions of a two-parameter family of harmonic quadrinomials. We also determine a curve that separates sensepreserving and sense-reversing regions for these families of quadrinomials. Our work makes practical and effective use of the work of Wilmshurst, Khavinson, Dehmer, and also Bezout’s Theorem in the plane.

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of ob...

This article proposes a method of management and control of a continuous bus powered by renewable energies for autonomous applications. The DC bus is obtained from two systems of renewable sources (the solar system and the wind system) and storage battery (Lithium Ion). The continuous bus control and management procedure require efficiency in the control of the charge and discharge of the battery according to the load energy demand (DC Motor). The battery charging process is non-linear, varying over time with considerable delay, so it is difficult to achieve the best performance on control with energy management using traditional control approaches. A fuzzy control strategy is used in this article for battery control. To improve battery life, fuzzy control manages the desired state of charge (SOC). The entire system designed is modeled and simulated on MATLAB/Simulink Environment.