Displaying publications 61 - 80 of 279 in total

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  1. Free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation
    Muhammad Khairul Anuar Mohamed, Nor Aida Zuraimi Md Noar, Mohd Zuki Salleh, Anuar Ishak
    Sains Malaysiana, 2016;45:189-296.
    In this paper, the problem of free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation and constant wall temperature is investigated. The transformed boundary layer equations are solved numerically using finite difference scheme namely the Keller-box method. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles.The features of the flow and heat transfer characteristics for various values of the Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number were analyzed and discussed.
    Matched MeSH terms: Motion
  2. Ion conductive polymer electrolyte membranes and simulation of their fractal growth patterns
    Amir S, Mohamed N, Hashim Ali S
    Sains Malaysiana, 2011;40:1123-1127.
    Due to their high ionic conductivity, solid polymer electrolyte (SPE) systems have attracted wide spread attention as the most appropriate choice to fabricate all-solid-state electrochemical devices, namely batteries, sensors and fuel cells. In this work, ion conductive polymer electrolyte membranes have been prepared for battery fabrication. However, fractals were found to grow in these polymer electrolyte membranes weeks after they were prepared. It was believed that the formation of fractal aggregates in these membranes were due to ionic movement. The discovery of fractal growth pattern can be used to understand the effects of such phenomenon in the polymer electrolyte membranes. Digital images of the fractal growth patterns were taken and a simulation model was developed based on the Brownian motion theory and a fractal dialect known as L-system. A computer coding has been designed to simulate and visualize the fractal growth.
    Matched MeSH terms: Motion
  3. An Interaction Model Based on An Interpretation of the First-Quantized Relativistic Schrodinger Equation
    Khalid Md. Nor, Ithnin Abdul Jalil, Hassan Abu Kasim
    Sains Malaysiana, 1996;25.
    The relativistic Schrodinger equation is reinterpreted as describing a classical particle that mutually-interacts with other objects via electromagnetic-like gravity waves. The accompanying derivation equates the usual quantum mechanical energy and momentum operators to the effects of negative or attractive energy. Lorentz-like transformation equations are obtained that yield the uncertainty principle such that quantum uncertainty is ascribed to the disregard of a magnetic-like component of a gravity wave. Finally, quantum-level Maxwell-like equations that involve the above gravity waves are derived.
    Persamaan Schrodinger kerelatifan ditafsirkan sebagai memperihalkan suatu zarah klasik yang berinteraksi dengan jasad-jasad lain melalui gelombang graviti yang berciri keelektromagnetan. Terbitan sampingan menyamakan pengoperasi-pengeoperasi tenaga dan momentum mekanik kuantum dengan kesan-kesan tenaga negatif atau tarikan. Persamaan-persamaan bermirip transformasi Lorentz diperolehi yang menerbitkan prinsip ketakpastian dan memberi ketakpastian kuantum sebagai kesan pengabaian bahagian gelombang graviti yang bermirip kemagnetan. Akhir sekali, persamaan-persamaan diparas kuntum yang bermirip persamaan-persamaan Maxwell diterbitkan dan melibatkan gelombang graviti yang tersebut di atas.
    Matched MeSH terms: Motion
  4. Parameter estimation of stochastic differential equation
    Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh
    Sains Malaysiana, 2012;41:1635-1642.
    Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochastic differential equation (SDE). The selection of knot and order of spline can be done heuristically based on the scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm was proposed. A single optimal knot is selected out of all the points with exception of the first and the last data which gives the least value of Generalized Cross Validation (GCV) for each order of spline. The use is illustrated using observed data of opening share prices of Petronas Gas Bhd. The results showed that the Mean Square Errors (MSE) for stochastic model with parameters estimated using optimal knot for 1,000, 5,000 and 10,000 runs of Brownian motions are smaller than the SDE models with estimated parameters using knot selected heuristically. This verified the viability of the two-step method in the estimation of the drift and diffusion parameters of SDE with an improvement of a single knot selection.
    Matched MeSH terms: Motion
  5. Currents simulation in the Malacca Straits by using three-dimensional numerical model
    Rizal S, Setiawan I, Ilhamsyah Y, Musman M, Iskandar T, Wahid MA
    Sains Malaysiana, 2010;39.
    The Malacca Straits is located between Peninsula Malaysia and Sumatra Island. This investigation used equation of motion (Navier-Stokes equation) with the following driving forces: tides, wind of National Centers for Environmental Prediction (NCEP) for year of 2007, salinity and temperature. The equation of motion was solved by means of Hamburg Shelf Ocean Model (HAMSOM). The results for both southwest and northeast monsoon were explained and discussed. The simulation results both for February and August 2007 were relatively similar. Current surface simulation in the Malacca Straits agrees well with the current pattern of previous works. The magnitude of current was between 10-70 cm/s to the northwest. While at the layer 30-50 m in the Malacca Straits, the currents have the magnitude of 10-30 cm/s towards northwest. For the bottom current, the current speed was 0-20 cm/s towards northwest. For the surface and 30-50 m layer, generally the current magnitudes were greater in February compared to those in August. While for the bottom layer, the current magnitudes between February and August were relatively the same.
    Matched MeSH terms: Motion
  6. Development of generalized feed forward network for predicting annual flood (depth) of a Tropical River
    Mohsen Salarpour, Milad Jajarmizadeh, Zulkifli Yusop, Fadhilah Yusof
    Sains Malaysiana, 2014;43:1865-1871.
    The modeling of rainfall-runoff relationship in a watershed is very important in designing hydraulic structures, controlling flood and managing storm water. Artificial Neural Networks (ANNs) are known as having the ability to model nonlinear mechanisms. This study aimed at developing a Generalized Feed Forward (GFF) network model for predicting annual flood (depth) of Johor River in Peninsular Malaysia. In order to avoid over training, cross-validation technique was performed for optimizing the model. In addition, predictive uncertainty index was used to protect of over parameterization. The governing training algorithm was back propagation with momentum term and tangent hyperbolic types was used as transfer function for hidden and output layers. The results showed that the optimum architecture was derived by linear tangent hyperbolic transfer function for both hidden and output layers. The values of Nash and Sutcliffe (NS) and root mean square error (RMSE) obtained 0.98 and 5.92 for the test period. Cross validation evaluation showed 9 process elements is adequate in hidden layer for optimum generalization by considering the predictive uncertainty index obtained (0.14) for test period which is acceptable.
    Matched MeSH terms: Motion
  7. Investigation of heat mass transfer for combined convective slips flow: a lie group analysis
    Md. Jashim Uddin, Md. Ismail A, Hamad M
    Sains Malaysiana, 2012;41:1139-1148.
    The steady laminar combined convective flow with heat and mass transfer of a Newtonian viscous incompressible fluid over a permeable flat plate with linear hydrodynamic and thermal slips has been investigated numerically. The velocity of the external flow, the suction/injection velocity and the temperature of the plate surface are assumed to vary nonlinearly following the power law with the distance along the plate from the origin. Lie group analysis is used to develop the similarity transformations and the governing momentum, the energy conservation and the mass conservation equations are converted to a system of coupled nonlinear ordinary differential equations with the associated boundary conditions. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. The effects of hydrodynamic slip parameter (a), thermal slip parameter (b), suction/injection parameter (fw), power law parameter (m), buoyancy ratio parameter (N), Prandtl number (Pr) and Schmidt number (Sc) on the fluid flow, heat transfer and mass transfer characteristics are investigated and presented graphically. We have also shown the effects of the Reynolds number (Re) and the power law parameter (m) on the velocity slip and the thermal slip factors. Good agreement is found between the numerical results of the present paper and published results.
    Matched MeSH terms: Motion
  8. Axisymmetric slip flow on a vertical cylinder with heat transfer
    Singh G, Makinde OD
    Sains Malaysiana, 2014;43:483-489.
    The paper is aimed at studying fluid flow heat transfer in the axisymmetric boundary layer flow of a viscous incompressible fluid, along the axial direction of a vertical stationary isothermal cylinder in presence of uniform free stream with momentum slip. The equations governing the flow i.e. continuity, momentum and energy equation are transformed into non-similar boundary layer equations and are solved numerically employing asymptotic series method with Shanks transformation. The numerical scheme involves the Runge-Kutta fourth order scheme along with the shooting technique. The flow is analyzed for both assisting and opposing buoyancy and the effect of different parameters on fluid velocity, temperature distribution, heat transfer and shear stress parameters is presented graphically.
    Matched MeSH terms: Motion
  9. Combined similarity-numerical solutions of MHD boundary layer slip flow of non-Newtonian power-law nanofluids over a radiating moving plate
    Nur Husna Md. Yusoff, Md. Jashim Uddin, Ahmad Izani Md. Ismail
    Sains Malaysiana, 2014;43:151-159.
    A combined similarity-numerical solution of the magnetohydrodynamic boundary layer slip flow of an electrically conducting non-Newtonian power-law nanofluid along a heated radiating moving vertical plate is explored. Our nanofluid model incorporates the influences of the thermophoresis and the Brownian motion. The basic transport equations are made dimensionless first and then suitable similarity transformations are applied to reduce them into a set of nonlinear ordinary differential equations with the associated boundary conditions. The reduced equations are then solved numerically. Graphical results for the non-dimensional flow velocity, the temperature and the nanoparticles volume fraction profiles as well as for the friction factor, the local Nusselt and the Sherwood numbers are exhibited and examined for various values of the controlling parameters to display the interesting aspects of the solutions. It was found that the friction factor increases with the increase of the magnetic field (M), whilst it is decreased with the linear momentum slip parameter (a). The linear momentum slip parameter (a) reduces the heat transfer rates and the nanoparticles volume fraction rates. Our results are compatible with the existing results for a special case.
    Matched MeSH terms: Motion
  10. Mixed convection flow of viscoelastic nanofluid past a horizontal circular cylinder with viscous dissipation
    Rahimah Mahat, Noraihan Afiqah Rawi, Sharidan Shafie, Abdul Rahman Mohd Kasim
    Sains Malaysiana, 2018;47:1617-1623.
    The purpose of this study was to examine the effect of viscous dissipation on mixed convection flow of viscoelastic
    nanofluid past a horizontal circular cylinder. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and
    copper as a nanoparticle with the Prandtl number Pr = 6.2. The transformed boundary layer equations for momentum
    and temperature subject to the appropriate boundary conditions are solved numerically by using Keller-box method. The
    influenced of the dimensionless parameters such as Eckert number, mixed convection parameter, nanoparticles volume
    fraction and viscoelastic parameter on the flow and heat transfer characteristics is analyzed in detail and presented
    graphically. The results come out with the velocity profiles are increased while the temperature profiles are decreased
    by increasing the values of nanoparticles volume fraction and viscoelastic parameter, respectively. The graph shows
    that, increasing Eckert number the skin friction is also increases. The values of skin friction are increased by increasing
    mixed convection parameter, but the values of Nusselt number produce an opposite behavior. The present study has many
    applications especially in heat exchangers technology and oceanography. Therefore, in future, it is hoping to study the
    viscoelastic nanofluid flow past a different geometric such as sphere and cylindrical cone.
    Matched MeSH terms: Motion
  11. Fulltext Angular velocity and elevation angle: the proposed human model scalable tracking model using linear regression
    Yong CY, Sudirman R, Chew KM
    Sains Malaysiana, 2015;44(12):1661-1669.
    A scalable tracking human model was proposed for recognizing human jogging and walking activities. The model aims to detect and track a particular subject by using wearable sensor. Data collected are in accelerometer readings in three axes and gyroscope readings in three axes. The development of proposed human model is based on the moderating effects on human movements. Two moderators were proposed as the moderating factors of human motion and they are angular velocity and elevation angle. Linear regression is used to investigate the relationship among inputs, moderators and outputs of the model. The result of this study showed that the angular velocity and elevation angle moderators are affecting the relation of research output. Acceleration in x-axis (Ax) and angular velocity in y-axis (Gy) are the two main components in directing
    a motion. Classification between jogging and walking motions was done by measuring the magnitude of angular velocity and elevation angle. Jogging motion was classified and identified with larger angular velocity and elevation angle. The two proposed hypotheses were supported and proved by research output. The result is expected to be beneficial and able to assist researcher in investigating human motions.
    Matched MeSH terms: Motion
  12. The influence of foot orthoses on foot mobility magnitude and arch height index in adults with flexible flat feet
    Sheykhi-Dolagh R, Saeedi H, Farahmand B, Kamyab M, Kamali M, Gholizadeh H, et al.
    Prosthet Orthot Int, 2015 Jun;39(3):190-6.
    PMID: 24604086 DOI: 10.1177/0309364614521652
    BACKGROUND: Flexible flat foot is described as a reduction in the height of the medial longitudinal arch and may occur from abnormal foot pronation. A foot orthosis is thought to modify and control excessive pronation and improve arch height.
    OBJECTIVE: To compare the immediate effect of three types of orthoses on foot mobility and the arch height index in subjects with flexible flat feet.
    STUDY DESIGN: A quasi-experimental study.
    METHOD: The dorsal arch height, midfoot width, foot mobility and arch height index were assessed in 20 participants with flexible flat feet (mean age = 23.2 ± 3 years) for three different foot orthosis conditions: soft, semi-rigid and rigid University of California Biomechanics Laboratory (UCBL).
    RESULTS: Maximum midfoot width at 90% with arch mobility in the coronal plane was shown in the semi-rigid orthosis condition. The semi-rigid orthosis resulted in the highest mean foot mobility in 90% of weight bearing, and the rigid orthosis (UCBL) had the lowest mean foot mobility. The soft orthosis resulted in foot mobility between that of the rigid and the semi-rigid orthosis. UCBL orthosis showed the highest arch height index, and the semi-rigid orthosis showed the lowest mean arch height index.
    CONCLUSION: Due to its rigid structure and long medial-lateral walls, the UCBL orthosis appears to limit foot mobility. Therefore, it is necessary to make an orthosis that facilitates foot mobility in the normal range of the foot arch. Future studies should address the dynamic mobility of the foot with using various types of foot orthoses.
    CLINICAL RELEVANCE: Although there are many studies focussed on flat foot and the use of foot orthoses, the mechanism of action is still unclear. This study explored foot mobility and the influence of foot orthoses and showed that a more rigid foot orthosis should be selected based on foot mobility.
    KEYWORDS: Foot orthosis; arch height index; foot mobility magnitude
    Matched MeSH terms: Range of Motion, Articular/physiology*
  13. Combined effects of knee brace, laterally wedged insoles, and toe-out gait on knee adduction moment and fall risk in moderate medial knee osteoarthritis patients
    Khan SJ, Khan SS, Usman J, Mokhtar AH, Abu Osman NA
    Prosthet Orthot Int, 2019 Apr;43(2):148-157.
    PMID: 30192706 DOI: 10.1177/0309364618796849
    BACKGROUND:: Knee osteoarthritis is a major contributor to the global burden of disease. There is a need of reducing knee joint load and to improve balance and physical function among knee osteoarthritis patients.

    OBJECTIVES:: To test the hypothesis that toe-out gait will reduce second peak knee adduction moment further and increase fall risk when combined with knee brace and laterally wedged insole in knee osteoarthritis patients.

    STUDY DESIGN:: Single visit study with repeated measures.

    METHODS:: First and second peak knee adduction moments, fall risk and comfort level. First and second peak knee adduction moments were determined from three-dimensional gait analysis, completed under six randomized conditions: (1) natural, (2) knee brace, (3) knee brace + toe-out gait, (4) laterally wedged insole, (5) laterally wedged insole + toe-out gait, and (6) knee brace + laterally wedged insole + toe-out gait. Fall risk was assessed by Biodex Balance System using three randomized stability settings: (1) static, (2) moderate dynamic setting (FR12), and (3) high dynamic setting (FR8).

    RESULTS:: The reduction in first peak knee adduction moment and second peak knee adduction moment was greatest (7.16% and 25.55%, respectively) when toe-out gait combine with knee brace and laterally wedged insole. Significant increase in fall risk was observed with knee brace + laterally wedged insole + toe-out gait (42.85%) at FR12. Similar significant balance reductions were found at FR8 condition for knee brace + toe-out gait (35.71%), laterally wedged insole + toe-out gait (28.57%), and knee brace + laterally wedged insole + toe-out gait (50%) as compared to natural. However, knee brace decreased fall risk at FR12 by 28.57%.

    CONCLUSION:: There is a synergistic effect of toe-out when combined with knee brace and laterally wedged insole concurrently in second peak knee adduction moment reduction but with a greater degree of fall risk. Simultaneous use of conservative treatments also decreases comfort level.

    CLINICAL RELEVANCE: Patients with mild and moderate knee osteoarthritis are usually prescribed conservative treatment techniques. This study will provide an insight whether or not a combination of these techniques have a synergistic effect in reducing knee joint load.

    Matched MeSH terms: Range of Motion, Articular/physiology*
  14. Fulltext Longitudinal, lateral and transverse axes of forearm muscles influence the crosstalk in the mechanomyographic signals during isometric wrist postures
    Islam MA, Sundaraj K, Ahmad RB, Sundaraj S, Ahamed NU, Ali MA
    PLoS One, 2014;9(8):e104280.
    PMID: 25090008 DOI: 10.1371/journal.pone.0104280
    In mechanomyography (MMG), crosstalk refers to the contamination of the signal from the muscle of interest by the signal from another muscle or muscle group that is in close proximity.
    Matched MeSH terms: Range of Motion, Articular/physiology
  15. Fulltext Conformational dynamics of dry lamellar crystals of sugar based lipids: an atomistic simulation study
    ManickamAchari V, Bryce RA, Hashim R
    PLoS One, 2014;9(6):e101110.
    PMID: 24978205 DOI: 10.1371/journal.pone.0101110
    The rational design of a glycolipid application (e.g. drug delivery) with a tailored property depends on the detailed understanding of its structure and dynamics. Because of the complexity of sugar stereochemistry, we have undertaken a simulation study on the conformational dynamics of a set of synthetic glycosides with different sugar groups and chain design, namely dodecyl β-maltoside, dodecyl β-cellobioside, dodecyl β-isomaltoside and a C12C10 branched β-maltoside under anhydrous conditions. We examined the chain structure in detail, including the chain packing, gauche/trans conformations and chain tilting. In addition, we also investigated the rotational dynamics of the headgroup and alkyl chains. Monoalkylated glycosides possess a small amount of gauche conformers (∼20%) in the hydrophobic region of the lamellar crystal (LC) phase. In contrast, the branched chain glycolipid in the fluid Lα phase has a high gauche population of up to ∼40%. Rotational diffusion analysis reveals that the carbons closest to the headgroup have the highest correlation times. Furthermore, its value depends on sugar type, where the rotational dynamics of an isomaltose was found to be 11-15% and more restrained near the sugar, possibly due to the chain disorder and partial inter-digitation compared to the other monoalkylated lipids. Intriguingly, the present simulation demonstrates the chain from the branched glycolipid bilayer has the ability to enter into the hydrophilic region. This interesting feature of the anhydrous glycolipid bilayer simulation appears to arise from a combination of lipid crowding and the amphoteric nature of the sugar headgroups.
    Matched MeSH terms: Motion
  16. Fulltext Conjugate effects of heat and mass transfer on MHD free convection flow over an inclined plate embedded in a porous medium
    Ali F, Khan I, Samiulhaq, Shafie S
    PLoS One, 2013;8(6):e65223.
    PMID: 23840321 DOI: 10.1371/journal.pone.0065223
    The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.
    Matched MeSH terms: Motion
  17. Fulltext Modelling pedestrian travel time and the design of facilities: a queuing approach
    Rahman K, Ghani NA, Kamil AA, Mustafa A, Kabir Chowdhury MA
    PLoS One, 2013;8(5):e63503.
    PMID: 23691055 DOI: 10.1371/journal.pone.0063503
    Pedestrian movements are the consequence of several complex and stochastic facts. The modelling of pedestrian movements and the ability to predict the travel time are useful for evaluating the performance of a pedestrian facility. However, only a few studies can be found that incorporate the design of the facility, local pedestrian body dimensions, the delay experienced by the pedestrians, and level of service to the pedestrian movements. In this paper, a queuing based analytical model is developed as a function of relevant determinants and functional factors to predict the travel time on pedestrian facilities. The model can be used to assess the overall serving rate or performance of a facility layout and correlate it to the level of service that is possible to provide the pedestrians. It has also the ability to provide a clear suggestion on the designing and sizing of pedestrian facilities. The model is empirically validated and is found to be a robust tool to understand how well a particular walking facility makes possible comfort and convenient pedestrian movements. The sensitivity analysis is also performed to see the impact of some crucial parameters of the developed model on the performance of pedestrian facilities.
    Matched MeSH terms: Time and Motion Studies*
  18. Fulltext Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect
    Bachok N, Ishak A, Pop I
    PLoS One, 2013;8(4):e60766.
    PMID: 23577156 DOI: 10.1371/journal.pone.0060766
    The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
    Matched MeSH terms: Motion*
  19. Fulltext Statistical predictions for the dynamics of a low-speed system: Newtonian versus special-relativistic mechanics
    Liang SN, Lan BL
    PLoS One, 2012;7(5):e36430.
    PMID: 22606259 DOI: 10.1371/journal.pone.0036430
    The newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic. The breakdown of agreement implies that special-relativistic mechanics must be used, instead of the standard practice of using newtonian mechanics, to correctly calculate the statistical predictions for the dynamics of a low-speed system.
    Matched MeSH terms: Motion
  20. Fulltext Newtonian versus special-relativistic statistical predictions for low-speed scattering
    Liang SN, Borondo F, Lan BL
    PLoS One, 2012;7(11):e48447.
    PMID: 23152774 DOI: 10.1371/journal.pone.0048447
    The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected. The predictions are close if the scattering is non-chaotic but they are radically different if the scattering is chaotic and the initial ensemble is well localized in phase space. Our result indicates that for low-speed chaotic scattering, special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empirically-correct statistical predictions from an initially well-localized Gaussian ensemble.
    Matched MeSH terms: Motion*
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