The Response of a SDOF System Driven by a Periodic Random Force

2017 ◽  
Vol 1144 ◽  
pp. 153-158
Author(s):  
Vladimír Sana ◽  
Ondrej Rokos ◽  
Jiří Maca
Keyword(s):  
Monte Carlo ◽  
Phase Shift ◽  
Equations Of Motion ◽  
Random Force ◽  
Mean Value ◽  
Newmark Method ◽  
Sdof System ◽  
Average Acceleration ◽  
The Mean ◽  
Duhamel’S Integral

This work deals with the response of a linear undamped SDOF system exposed to a force with random amplitude, phase shift, or their combination. The first two moments, the mean value and the variance, of the response will be determined analytically through the Duhamel's integral, and compared to the numerical Monte Carlo simulations. Integration of associated equations of motion will be performed by the Newmark method of average acceleration.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

scholarly journals Evaluation of Bearing Capacity of Strip Footing Using Random Layers Concept

2015 ◽  
Vol 37 (3) ◽  
pp. 31-39 ◽  
Author(s):  
Marek Kawa ◽  
Dariusz Łydżba
Keyword(s):  
Monte Carlo ◽  
Bearing Capacity ◽  
Failure Mechanism ◽  
Design Theory ◽  
Cohesive Soil ◽  
Probability Of Failure ◽  
Mean Value ◽  
Strip Footing ◽  
Random Field Theory ◽  
The Mean

Abstract The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

Reduced conformal geometrodynamics

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040023 ◽  
Author(s):  
Andrej B. Arbuzov ◽  
Alexander E. Pavlov
Keyword(s):  
Gravitational Field ◽  
Dynamical Systems ◽  
Coordinate System ◽  
Tangent Space ◽  
Equations Of Motion ◽  
Mean Value ◽  
Hamiltonian Reduction ◽  
Square Root ◽  
The Mean ◽  
Static Background

The global time in geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The reduced Hamiltonian equations of motion of gravitational field in semi-geodesic coordinate system are written.

scholarly journals Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg

2021 ◽  
Vol 25 (1) ◽  
pp. 193-216
Author(s):  
Jairo Arturo Torres-Matallana ◽  
Ulrich Leopold ◽  
Gerard B. M. Heuvelink
Keyword(s):  
Water Quality ◽  
Monte Carlo ◽  
Uncertainty Propagation ◽  
Mean Value ◽  
Water Quantity ◽  
Urban Drainage ◽  
Urban Water ◽  
The Mean ◽  
Input Variables

Abstract. Uncertainty is often ignored in urban water systems modelling. Commercial software used in engineering practice often ignores the uncertainties of input variables and their propagation because of a lack of user-friendly implementations. This can have serious consequences, such as the wrong dimensioning of urban drainage systems (UDSs) and the inaccurate estimation of pollution released to the environment. This paper introduces an uncertainty analysis in urban drainage modelling, built on existing methods and applied to a case study in the Haute-Sûre catchment in Luxembourg. The case study makes use of the EmiStatR model which simulates the volume and substance flows in UDS using simplified representations of the drainage system and processes. A Monte Carlo uncertainty propagation analysis showed that uncertainties in chemical oxygen demand (COD) and ammonium (NH4) loads and concentrations can be large and have a high temporal variability. Furthermore, a stochastic sensitivity analysis that assesses the uncertainty contributions of input variables to the model output response showed that precipitation has the largest contribution to output uncertainty related with water quantity variables, such as volume in the chamber, overflow volume, and flow. Regarding the water quality variables, the input variable related to COD in wastewater has an important contribution to the uncertainty for the COD load (66 %) and COD concentration (62 %). Similarly, the input variable related to NH4 in wastewater plays an important role in the contribution of total uncertainty for the NH4 load (34 %) and NH4 concentration (35 %). The Monte Carlo (MC) simulation procedure used to propagate input uncertainty showed that, among the water quantity output variables, the overflow flow is the most uncertain output variable, with a coefficient of variation (cv) of 1.59. Among water quality variables, the annual average spill COD concentration and the average spill NH4 concentration were the most uncertain model outputs (coefficients of variation of 0.99 and 0.82, respectively). Also, low standard errors for the coefficient of variation were obtained for all seven outputs. These were never greater than 0.05, which indicates that the selected MC replication size (1500 simulations) was sufficient. We also evaluated how the uncertainty propagation can more comprehensively explain the impact of water quality indicators for the receiving river. While the mean model water quality outputs for COD and NH4 concentrations were slightly above the threshold, the 0.95 quantile was 2.7 times above the mean value for COD concentration and 2.4 times above the mean value for NH4. This implies that there is a considerable probability that these concentrations in the spilled combined sewer overflow (CSO) are substantially larger than the threshold. However, COD and NH4 concentration levels of the river water will likely stay below the water quality threshold, due to rapid dilution after CSO spill enters the river.

On Monte Carlo Estimates in Network Reliability

1994 ◽  
Vol 8 (2) ◽  
pp. 245-264 ◽  
Author(s):  
M. Lomonosov
Keyword(s):  
Monte Carlo ◽  
Markov Process ◽  
Critical Point ◽  
Natural Condition ◽  
Network Reliability ◽  
Random Variable ◽  
Mean Value ◽  
Reliability Measures ◽  
The Mean ◽  
Edge Failure

The paper considers representations of network reliability measures as the mean value of a random variable defined on the trajectories of a certain Markov process and investigates utility of such formulae for Monte Carlo (MC) estimating. Such an MC estimator is called (ε,δ)-polynomial if its relative error is less than ε with probability >1 – δ, for any sample size equal to or greater than a polynomial of ε-1, δ-1, and the size of the network. One of the main results: The suggested MC estimator for the disconnectedness probability of a multiterminal network is (ε,δ)-polynomial, under a certain natural condition on the edge failure probabilities. The method applies also to estimating the percolation critical point and certain equilibrium characteristics of renewal networks.

scholarly journals Multivariate autoregressive modelling and conditional simulation for temporal uncertainty propagation in urban water systems

2020 ◽  
Author(s):  
Jairo Arturo Torres-Matallana ◽  
Ulrich Leopold ◽  
Gerard B. M. Heuvelink
Keyword(s):  
Water Quality ◽  
Monte Carlo ◽  
Uncertainty Propagation ◽  
Water Systems ◽  
Mean Value ◽  
Water Quantity ◽  
Urban Drainage ◽  
Urban Water ◽  
The Mean ◽  
Input Variables

Abstract. Uncertainty is often ignored in urban water systems modelling. Commercial software used in engineering practice often ignores uncertainties of input variables and their propagation because of a lack of user-friendly implementations. This can have serious consequences, such as the wrong dimensioning of urban drainage systems (UDS) and the inaccurate estimation of pollution released to the environment. This paper introduces an uncertainty analysis framework in urban drainage modelling and applies it to a case study in the Haute-Sûre catchment in Luxembourg. The framework makes use of the EmiStatR model which simulates the volume and substance flows in UDS using simplified representations of the drainage system and processes. A Monte Carlo uncertainty propagation analysis showed that uncertainties in chemical oxygen demand (COD) and ammonium (NH4) loads and concentrations can be large and have a high temporal variability. Further, a stochastic sensitivity analysis that assesses the uncertainty contributions of input variables to the model output response showed that precipitation has the largest contribution to output uncertainty related with water quantity variables, such as volume in the chamber, overflow volume and flow. Regarding the water quality variables, the input variable related to COD in the wastewater has an important contribution to the uncertainty for COD load (66 %) and COD concentration (62 %). Similarly, the input variable related to NH4 in the wastewater plays an important role in the contribution of total uncertainty for NH4 load (34 %) and NH4 concentration (35 %). The Monte Carlo simulation procedure used to propagate input uncertainty showed that among the water quantity output variables, the overflow flow is the most uncertain output variable with a coefficient of variation (cv) of 1.59. Among water quality variables, the annual average spill COD oncentration and the average spill NH4 concentration were the most uncertain model outputs (coefficients of variation of 0.99 and 0.82, respectively). Also, low standard errors for the coefficient of variation were obtained for all seven outputs. These were never greater than 0.05, which indicates that the selected MC replication size (1,500 simulations) was sufficient. We also evaluated how uncertainty propagation can explain more comprehensively the impact of water quality indicators for the receiving river. While the mean model water quality outputs for COD and NH4 concentrations were slightly above the threshold, the 0.95 quantile was 2.7 times above the mean value for COD concentration, and 2.4 times above the mean value for NH4. This implies that there is a considerable probability that these concentrations in the spilled CSO are substantially larger than the threshold. However, COD and NH4 concentration levels of the river water will likely stay below the water quality threshold, due to rapid dilution after CSO spill enters the river.

scholarly journals Longitudinal impedance of single frog muscle fibers.

1975 ◽  
Vol 65 (1) ◽  
pp. 97-113 ◽  
Author(s):  
B A Mobley ◽  
J Leung ◽  
R S Eisenberg
Keyword(s):  
Skeletal Muscle ◽  
Phase Shift ◽  
Muscle Fibers ◽  
Mean Value ◽  
Sartorius Muscle ◽  
Semitendinosus Muscle ◽  
Skeletal Muscle Fibers ◽  
Longitudinal Impedance ◽  
Small Phase ◽  
The Mean

The longitudinal impedance of single skeletal muscle fibers has been measured from1 to 10,000 Hz in an oil gap apparatus which forces current to flow longitudinally down the fiber. The impedance observed is purely resistive in some fibers from the semitendinosus muscle and in two fibers from the sartorius muscle. In other fibers from the semitendinosus muscle a small phase shift is observed. The mean value of the maximum phase shift observed from all fibers is 1.07 degrees. The artifacts associated with the apparatus and method are examined theoretically and it is shown that one of the likely artifacts could account for the small phase observed. It is concluded that the longitudinal impedance of skeletal muscle fibers is essentially resistive and that little, if any, longitudinal current crosses the membranes of the sarcoplasmic reticulum.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

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