Lambertian Enclosures — A First Step towards Fast Room Acoustics Simulation

2003 ◽  
Vol 10 (1) ◽  
pp. 33-54 ◽  
Author(s):  
D. Alarcão ◽  
J. L. Bento Coelho
Keyword(s):  
Integral Equation ◽  
Markov Chain ◽  
Steady State ◽  
Statistical Method ◽  
Room Acoustics ◽  
Homogeneous Markov Chain ◽  
Acoustical Parameters ◽  
First Order ◽  
Time Discretisation ◽  
Reflecting Boundaries

A statistical method for calculation of the acoustical parameters of lambertian enclosures (that is, enclosures with diffusely reflecting boundaries) is presented. The theory considers the distribution of sound particles over the boundaries of the enclosures. The method includes the familiar Kuttruff Integral Equation. A homogeneous Markov Chain of first order is obtained through the time discretisation of the equations. Applications of this method are demonstrated for the case of a long enclosure and for the case of a real-shaped room. Decay calculations as well as steady-state sound distributions are obtained. The results show that the method is reliable, flexible, and that computation times are low.

The Spectrum of Steady State Turbulent Convection

1971 ◽  
Vol 26 (7) ◽  
pp. 1140-1146
Author(s):  
F. Winterberg
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
Energy Spectrum ◽  
Buoyancy Force ◽  
Radiative Heat ◽  
Order Differential Equation ◽  
Stellar Atmospheres ◽  
Turbulent Convection ◽  
First Order ◽  
Model Equations

Abstract Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

CAN MARKOV CHAIN MODELS MIMIC BIOLOGICAL REGULATION?

2002 ◽  
Vol 10 (04) ◽  
pp. 337-357 ◽  
Author(s):  
SEUNGCHAN KIM ◽  
HUAI LI ◽  
EDWARD R. DOUGHERTY ◽  
NANWEI CAO ◽  
YIDONG CHEN ◽  
...  
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Regulatory Network ◽  
Original Data ◽  
The State ◽  
Biological Behavior ◽  
Model Parameters ◽  
Sufficient Information ◽  
Homogeneous Markov Chain ◽  
Finite State

A fundamental question in biology is whether the network of interactions that regulate gene expression can be modeled by existing mathematical techniques. Studies of the ability to predict a gene's state based on the states of other genes suggest that it may be possible to abstract sufficient information to build models of the system that retain steady-state behavioral characteristics of the real system. This study tests this possibility by: (i) constructing a finite state homogeneous Markov chain model using a small set of interesting genes; (ii) estimating the model parameters based on the observed experimental data; (iii) exploring the dynamics of this small genetic regulatory network by analyzing its steady-state (long-run) behavior and comparing the resulting model behavior to the observed behavior of the original system. The data used in this study are from a survey of melanoma where predictive relationships (coefficient of determination, CoD) between 587 genes from 31 samples were examined. Ten genes with strong interactive connectivity were chosen to formulate a finite state Markov chain on the basis of their role as drivers in the acquisition of an invasive phenotype in melanoma cells. Simulations with different perturbation probabilities and different iteration times were run. Following convergence of the chain to steady-state behavior, millions of samples of the results of further transitions were collected to estimate the steady-state distribution of network. In these samples, only a limited number of states possessed significant probability of occurrence. This behavior is nicely congruent with biological behavior, as cells appear to occupy only a negligible portion of the state space available to them. The model produced both some of the exact state vectors observed in the data, and also a number of state vectors that were near neighbors of the state vectors from the original data. By combining these similar states, a good representation of the observed states in the original data could be achieved. From this study, we find that, in this limited context, Markov chain simulation emulates well the dynamic behavior of a small regulatory network.

Runway Utilization Analysis Based on the Stochastic Petri Net Model

2013 ◽  
Vol 411-414 ◽  
pp. 1750-1756
Author(s):  
Gao Yang Jiang ◽  
Jie Ning Wang ◽  
Chun Feng Zhang ◽  
Mei Dong
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Petri Net ◽  
Simulation Method ◽  
State Probability ◽  
Homogeneous Markov Chain ◽  
Steady State Probability ◽  
Stochastic Petri Net ◽  
Markov Chain Method ◽  
Key Indicators

Runway utilization is one of the key indicators of airport operational efficiency. Firstly, stochastic Petri net was introduced to built runway system operational model, and then we analyzed the reachability graph of this model, which not only prove the reachability and boundedness of this model, but also can be used to transform to homogeneous Markov chain. Secondly, The system steady-state probability expressions in various states were established based on the homogeneous Markov chain. Thirdly, runway utilization was calculated based on the steady-state probability expressions. During simulation, runway utilizations in various conditions were analyzed by changing some transitions fire rate. Both Markov chain method and petri net simulation method are useful for runway utilization improvement.

scholarly journals The Markov Chain Market

2003 ◽  
Vol 33 (02) ◽  
pp. 265-287 ◽  
Author(s):  
Ragnar Norberg
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Homogeneous Markov Chain ◽  
Risk Minimization ◽  
Interest Rate Derivatives ◽  
First Order ◽  
Chain Conditions ◽  
The Matrix ◽  
Market Driven ◽  
Absence Of Arbitrage

We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.

scholarly journals The Markov Chain Market

2003 ◽  
Vol 33 (2) ◽  
pp. 265-287 ◽  
Author(s):  
Ragnar Norberg
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Homogeneous Markov Chain ◽  
Risk Minimization ◽  
Interest Rate Derivatives ◽  
First Order ◽  
Chain Conditions ◽  
The Matrix ◽  
Market Driven ◽  
Absence Of Arbitrage

We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.

Statistical method of steepest improvement of response

2018 ◽  
Vol 84 (11) ◽  
pp. 74-87
Author(s):  
V. B. Bokov
Keyword(s):  
Statistical Method ◽  
Linear Model ◽  
Response Prediction ◽  
Initial Experiment ◽  
First Order ◽  
Prediction Response ◽  
Conditional Extremum ◽  
Order Polynomial ◽  
Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

Nappes d'huile: prediction de leurs deplacements comme agent efficace d'un plan de mesure d'urgence

1979 ◽  
Vol 14 (1) ◽  
pp. 89-109
Author(s):  
B. Coupal ◽  
M. de Broissia
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Finite Elements ◽  
Mass Balance ◽  
Stochastic Method ◽  
Stochastic Methods ◽  
Deterministic Approach ◽  
First Order ◽  
The Third ◽  
Comme Agent

Abstract The movement of oil slicks on open waters has been predicted, using both deterministic and stochastic methods. The first method, named slick rose, consists in locating an area specifying the position of the slick during the first hours after the spill. The second method combines a deterministic approach for the simulation of current parameters to a stochastic method simulating the wind parameters. A Markov chain of the first order followed by a Monte Carlo approach enables the simulation of both phenomena. The third method presented in this paper describes a mass balance on the spilt oil, solved by the method of finite elements. The three methods are complementary to each other and constitute an important point for a contingency plan.

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