Correct Mathematical Model Research Articles

Design and Modeling on Stranded Wires Helical Springs

A stranded wires helical spring is formed of a multilayer and coaxial strand of several wires twisted together with the same direction of spiral. Compared with the conventional single wire spring, the stranded wires helical spring has the notable predominance in strength, damping and vibration reduction, which is usually used in aircraft engines, automatic weapons, etc. However, due to its complicated structure, the precise computation of its strength and rigidity need be a correct mathematical model, which then will be imported to finite element analysis software for solutions. Equations on solving geometric parameters, such as external diameters of strands and screw pitches of wires, are put forward in the paper. It also proposes a novel methodology on solving geometric parameters and establishing entity models of the stranded wires helical spring, which provides foundation of computing mechanical parameters by FEA. Then mathematical models on the centre line of the strand and the surface curve of each wire, after closing two ends in a spring, are proposed. Finally, geometric parameters are solved in a case study, and a 3D entity model of a spring with 3 layers and 16 wires is established, which has validated the accuracy of the proposed methodology and the 3D entity mathematical model. The method provides a new way to design stranded wire helical spring.

Transport effects on surface reaction arrays: Biosensor applications

The ubiquity of surface-volume reactions in biological and industrial processes makes knowledge of their kinetics critical. This has spurred technological advances in several biosensors designed to measure rate constants, such as the Flexchip and the dotLab. These biosensors have multiple reacting zones in a single flow channel, and hence they also serve as good model systems for biochemical systems with multiple reacting zones, such as cell membranes. A correct mathematical model for such systems must incorporate the effects of transport and zone position. A basic unidirectional flow model is developed in general and solved for typical experimental parameters using perturbation methods. The effect of zone placement along the channel can be quantified in terms of an effective Damköhler number based upon position. Moreover, it is established that zone placement across the channel does not affect the measurements.

Approximation of the observed motion of bolides by the analytical solution of the equations of meteor physics

A great volume of data has been accumulated thus far related to the photoregistration of the paths of meteor bodies in the terrestrial atmosphere. Most images have been obtained by four bolide networks, which operate in the USA, Canada, Europe, and Spain in different time periods. The approximation of the actual data using theoretical models makes it possible to achieve additional estimates, which do not directly follow from the observations. In the present study, we suggest an algorithm to find such parameters of the theoretical relationship between the height and the velocity of the bolide motion that help to fit observations along the luminous part of the trajectories in the best way. The main difference from previous studies is that the given observations are approximated using the analytical solution of the equations of meteor physics. The model presented in this study was applied to a number of bright meteors observed by the Canadian camera network and by the US Prairie network and to the Benesov bolide, which is one of the largest fireballs registered by the European network. The correct mathematical modeling of meteor events in the atmosphere is necessary for further estimates of the key parameters, including the extra-atmospheric mass, the ablation coefficient, and the effective enthalpy of evaporation of entering bodies. In turn, this information is needed by some applications, namely, those aimed at studying the problems of asteroid and comet security, to develop measures of planetary defense, and to determine the bodies that can reach Earth’s surface.

On the theory of thin bodies

It is shown that, in accordance with the law of plane sections representing the basis of the theory of thin bodies, two analogies are true: a nonstationary analogy and a stationary one. Within the framework of the stationary analogy, a new-type expansion reducing a three-dimensional problem to a stationary two-dimensional one is introduced. The asymptotic conditions of validity of the stationary and nonstationary analogies were determined and the boundary-layer conceptions for both cases were compared. Solutions of the internal and external problems on a two-dimensional flow in a narrow zone were obtained in the closed form. An asymptotically correct mathematical model of a flow in a film is proposed. The stationary and nonstationary analogies for a swirling flow around a body and a flow around a rotating body were determined.

Surgical Modelling, Simulation and Education

Soft tissue simulation is an important technique in many biomedical modelling applications. While applications for investigating the functioning of organs do require a physically correct mathematical model, other tasks, such as virtual surgery simulations for training purposes, put a bigger emphasis on speed, ease of use, and a large variety of arbitrary interaction. In such applications a plausible, physically not accurate technique is often sufficient. We have investigated the use of meshless deformation based on shape matching for soft tissue simulation and we implemented several improvements which make the simulation more accurate and stable. Novel interaction techniques such as fast, interactive cutting, pushing and picking are introduced. The method is very efficient, easily implemented, and can be integrated into graphics and game engines, but has restrictions in the range of simulated objects.

Rival approaches to mathematical modelling in immunology

In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

High-resolution gas volume change measurements bring new insights in pressure regulation of the middle ear

in this issue, the paper by Kania et al. ([7][1]) presents measurements and modeling results on the role of nitrogen in the gas exchange processes in the middle ear. The middle ear is a semirigid biological gas pocket that is closed most of the time. External influences, such as changing weather

Theoretical Solutions for Finite-Span Wings of Arbitrary Shapes Using Velocity Singularities

This paper presents a new method of solution for the e nite-span wings of arbitrary shapes, which avoids the dife culties of the previous methods. This method uses velocity singularities in the Trefftz plane to derive the contributions in the solution of the circulation distribution caused by the changes in the spanwise variation of the wing chord and incidence. The new functions derived for these contributions contain both natural and forced symmetry and antisymmetry terms (which are absent in the previous methods ) and thus represent a correct mathematical modeling of the physical problemsthat lead to highly accurate theoretical solutions. The method has beenvalidatedbycomparisonwiththesolutionsobtainedbyRasmussenandSmithandCarafoliforrectangularand tapered wings of uniform incidence, and with the panel method results by Katzand Plotkin. Accurateand efe cient theoretical solutions of aeronautical interest are then obtained for wings with asymmetric incidence distributions caused by symmetric and antisymmetric dee ections of e aps and ailerons and for wings with curved leading and trailing edges and variable incidence, which are dife cult to model in current panel methods.

Numerical simulations of low-velocity impact on an aircraft sandwich panel

The potential hazards resulting from a low-velocity impact (bird-strike, tool drop, runway debris, etc.) on aircraft structures, such as engine nacelle or a leading edge, has been a long-term concern to the aircraft industry. Certification authorities require that exposed aircraft components must be tested to prove their capability to withstand low-velocity impact without suffering critical damage. This paper describes the results from experimental and numerical simulation studies on the impact and penetration damage of a sandwich panel by a solid, round-shaped impactor. The main aim was to prove that a correct mathematical model can yield significant information for the designer to understand the mechanism involved in the low-velocity impact event, prior to conducting tests, and therefore to design an impact-resistant aircraft structure. Part of this work presented is focused on the recent progress on the materials modelling and numerical simulation of low-velocity impact response onto a composite aircraft sandwich panel. It is based on the application of explicit finite element (FE) analysis codes to study aircraft sandwich structures behaviour under low-velocity impact conditions. Good agreement was obtained between numerical and experimental results, in particular, the numerical simulation was able to predict impact damage and impact energy absorbed by the structure.

Hyperfinite type structures

The notion of a hyperfinite set comes from nonstandard analysis. Such a set has the internal cardinality of a nonstandard natural number. By a transfer principle such sets share many properties of finite sets. Here we apply this notion to give a hyperfinite model of the Kleene-Kreisel continuous functionals. We also extend the method to provide a hyperfinite characterisation of certain transfinite type structures, thus, through the work of Waagbø [14], constructing a hyperfinite model for Martin-Löf type theory.This kind of application is not new. Normann [6] gave a characterisation of the Kleene-Kreisel continuous functionals using ‘hyperfinitary’ functionals. The novelty here is that we use a constructive version of hyperfinite functionals and also generalise the method to transfinite types. Many of the results of this paper are constructive, though not the characterisation theorems themselves.Our characterisation of the Kleene-Kreisel continuous functionals is a supplement to a number of previous characterisations of topological and recursion-theoretical nature, see [6] for a brief survey. Altogether these characterisations show that the original concept of Kleene and Kreisel forms the correct mathematical model of the idea of finitely based functions of finite types.There is, however, no a priori reason to believe that there is a canonical way to extend the continuous functionals to cover transfinite objects of transfinite type used in, e.g., type theory. Our characterisation of Waagbø's model indicates that the model is natural, not only seen from domain theory but from a higher perspective. Normann and Waagbø (unpublished) have subsequently obtained a limit-space characterisation that further supports this view.

Adaptive Finite Elements for Elastic Bodies in Contact

To avoid interpenetration of matter under the small strain assumption, the linear contact condition is frequently applied where the distance of bodies is controlled only along a certain direction. The standard direction is the normal on the surface where interpenetration might occur. In this paper we allow other directions as well. We address questions such as the correct mathematical model, existence of solutions, the penalty method for regularization of the variational inequality, finite element discretization, and a priori and a posteriori error estimates, but exclude the error of penalization. The computable upper error bound leads to a criterion for automatic mesh-refinements within a finite element method. Numerical simulations of the Hertzian contact problem and a supported cantilever beam are included.

Modelling and analysis of time-lags in some basic patterns of cell proliferation.

In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.

Modeling of Transport Processes in the Presence of Substance-Locking Effects

Mass-transport processes under the action of an external field in a medium with piecewise-constant properties and special equations of state are investigated both analytically and numerically. An analytical solution of hyperbolic conservation law on which some algebraic restrictions are imposed is presented. Special emphasis is given to the construction of a correct mathematical model for transport processes. The technique of solving the generalized Riemann problem with two initial discontinuities is developed and rigorously revised. The influence of diffusion effects on the solution profile, especially in the vicinity of a stationary contact discontinuity, is studied by numerical methods. An example of a real mass-transport process under the impact of an external force in which a part of the substance is entrapped between stationary discontinuities is presented. This physical effect was observed experimentally for the first time by the authors in electrophoresis---a separation method for chemically reactive multicomponent mixtures by means of an applied electric field.

Biological response to blast overpressure: A summary of modeling

A soldier in training is exposed to a variety of blast sources that can adversely affect his auditory and nonauditory systems. While auditory standards have been formulated for many decades, knowledge about nonauditory effects of blast have not been captured in a criterion that can be applied to all circumstances. For the past 15 years, JAYCOR, working together with the Walter Reed Army Institute of Research, has been using modeling, simulation, and data analysis to determine the nature of injury in animal models, capture that understanding in physiologically correct mathematical models, and extend the findings to objective criteria that can be used to set exposure limits. This paper summarizes the accomplishments of that effort.

Simplified mathematical model of irreversible sample adsorption in capillary zone electrophoresis

In this paper, a very simple mathematical model of the irreversible adsorption of a sample onto the capillary wall in capillary zone electrophoresis is investigated analytically and numerically. With it, the influence of adsorption on the transport of sample is studied. The advantage of the model is that it contains only one parameter while other models usually contain many more. Mathematically, the problem is reduced to the construction of a solution of a partial differential equation coupled to an algebraic equation that imposes some restriction on the solution. Great attention is paid to the formulation of a correct mathematical model of the process. In diffusionless approximation, an analytical solution is obtained, while the influence of diffusion is studied by computer simulation. It is shown that in diffusionless approximation, the qualitative results regarding the behavior of the sample zone have a rather general character and do not depend on the specific mechanism of interaction between the substance and the wall.

The Meyer model revisited: why is charge not conserved? (MOS transistor)

A new approach to computer simulation of capacitance effects in MOS transistors is presented. It is shown that charge nonconservation is the result of faulty mathematical modeling of the capacitive nonlinearities in the SPICE circuit simulator and is not intrinsic to any specific charge or capacitance model. The correct mathematical model is described. The results of computer simulations using the Meyer capacitance model, which conserves charge, are given for some test circuits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Solar variability due to sunspots and faculae

Results of photometry of solar active regions and their effect on the solar irradiance in the visible part of the spectrum are presented. The effects of sunspots and faculae are given separately, since the measurement of sunspot irradiance fluctuations is less uncertain. It is argued that energy balance may exist between sunspot deficits and facular excesses. The uncertainty however, is ±15% (1σ). This possible balance also depends on the correct mathematical model for the contrast of faculae as a function of position on the solar disk. Extreme Limb Photometer (ELP) data are presented in such a way as to show that the model for facular limb darkening is consistent with the assumptions inherent in the irradiance modeling. The ELP data support the notion that energy balance between spots and faculae is possible. It is emphasized that even if there is energy balance, there will still be variations in the solar irradiance at the earth.