Statistical Model for the Inherent Tilt of Flip-Chips

1996 ◽  
Vol 118 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Lewis S. Goldmann
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Statistical Model ◽  
Closed Form ◽  
High Power ◽  
Power Electronic ◽  
Mathematical Algorithm ◽  
Flip Chips ◽  
Statistical Variation ◽  
Analytical Tools

The tilt of flip-chips is becoming increasingly important in optical and high-power electronic applications. This paper outlines the principal sources of tilt, and presents a mathematical algorithm for the statistical variation in inherent tilt, the component related to variability of solder pad dimensions. With the assistance of a Monte Carlo simulation, closed form equations are developed for several common families of symmetric pad footprints. Possible extension of the analytical tools to other important cases is discussed.

scholarly journals Statistical Mechanics of Discrete Multicomponent Fragmentation

2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Themis Matsoukas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Closed Form ◽  
Fixed Number ◽  
Arbitrary Degree ◽  
Fragment Distribution ◽  
The Mean ◽  
Fragmentation Event

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

Monte Carlo simulation of high power microwave window breakdown at atmospheric conditions

2006 ◽  
Vol 89 (20) ◽  
pp. 201501 ◽  
Author(s):  
John T. Krile ◽  
Andreas A. Neuber ◽  
Hermann G. Krompholz ◽  
Thomas L. Gibson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
High Power ◽  
Atmospheric Conditions ◽  
High Power Microwave ◽  
Power Microwave

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

2021 ◽  
Vol 14 (2) ◽  
pp. 183-193
Author(s):  
Abdul Hoyyi ◽  
Abdurakhman Abdurakhman ◽  
Dedi Rosadi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Form ◽  
Stock Price ◽  
Option Price ◽  
Secondary Data ◽  
Exponential Model ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Normally Distributed

The Option is widely applied in the financial sector.  The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the  process exponential model. The  process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the  process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK).  The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various  values until convergent result was obtained.

Improved Current Statistic Model and Adaptive Filtering

2005 ◽  
Author(s):  
Hongtao Hu ◽  
Zhongliang Jing
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Statistical Model ◽  
Adaptive Filtering ◽  
Adaptive Algorithm ◽  
Tracking Algorithm ◽  
Unscented Transformation ◽  
Maneuvering Targets ◽  
Statistic Model ◽  
Simulation Results

Current statistical model needs to pre-define the value of maximum accelerations of maneuvering targets. So it may be difficult to meet all maneuvering conditions. In this paper a novel adaptive algorithm for tracking maneuvering targets is proposed. The algorithm is implemented with fuzzy-controlled current statistic model adaptive filtering and unscented transformation. The Monte Carlo simulation results show that this method outperforms the conventional tracking algorithm based on current statistical model.

scholarly journals Duality Between the Two-Locus Wright–Fisher Diffusion Model and the Ancestral Process with Recombination

2013 ◽  
Vol 50 (01) ◽  
pp. 256-271 ◽  
Author(s):  
Shuhei Mano
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Diffusion Process ◽  
Closed Form ◽  
Numerical Method ◽  
Diffusion Model ◽  
Ancestral Recombination Graph ◽  
Duality Argument

Known results on the moments of the distribution generated by the two-locus Wright–Fisher diffusion model, and the duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical method for computing moments using a Markov chain Monte Carlo simulation and a method to compute closed-form expressions of the moments are presented. By applying the duality argument, the properties of the ancestral recombination graph are studied in terms of the moments.

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