The Hermite function expansions of the Heaviside function

2015 ◽  
Vol 6 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Toshinao Kagawa
Keyword(s):  
Heaviside Function ◽  
Hermite Function

scholarly journals A Cloud Microphysics Parameterization for Shallow Cumulus Clouds Based on Lagrangian Cloud Model Simulations

2018 ◽  
Vol 75 (11) ◽  
pp. 4031-4047 ◽  
Author(s):  
Yign Noh ◽  
Donggun Oh ◽  
Fabian Hoffmann ◽  
Siegfried Raasch
Keyword(s):  
Cloud Model ◽  
Cloud Microphysics ◽  
Heaviside Function ◽  
Mixing Ratio ◽  
Cumulus Clouds ◽  
Cloud Droplets ◽  
Shallow Cumulus ◽  
Initial Stage ◽  
Accretion Rates ◽  
The Moment

Abstract Cloud microphysics parameterizations for shallow cumulus clouds are analyzed based on Lagrangian cloud model (LCM) data, focusing on autoconversion and accretion. The autoconversion and accretion rates, A and C, respectively, are calculated directly by capturing the moment of the conversion of individual Lagrangian droplets from cloud droplets to raindrops, and it results in the reproduction of the formulas of A and C for the first time. Comparison with various parameterizations reveals the closest agreement with Tripoli and Cotton, such as and , where and are the mixing ratio and the number concentration of cloud droplets, is the mixing ratio of raindrops, is the threshold volume radius, and H is the Heaviside function. Furthermore, it is found that increases linearly with the dissipation rate and the standard deviation of radius and that decreases rapidly with while disappearing at > 3.5 μm. The LCM also reveals that and increase with time during the period of autoconversion, which helps to suppress the early precipitation by reducing A with smaller and larger in the initial stage. Finally, is found to be affected by the accumulated collisional growth, which determines the drop size distribution.

scholarly journals Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models

2016 ◽  
Author(s):  
Huda Mohd. Ramli ◽  
J. Gavin Esler
Keyword(s):  
Planck Equation ◽  
Particle Dispersion ◽  
Test Problems ◽  
Hermite Function ◽  
Dispersion Models ◽  
Lagrangian Particle ◽  
Integration Schemes ◽  
Fokker Planck Equation ◽  
Long Time ◽  
Fokker Planck

Abstract. A rigorous methodology for the evaluation of integration schemes for Lagrangian particle dispersion models (LPDMs) is presented. A series of one-dimensional test problems are introduced, for which the Fokker-Planck equation is solved numerically using a finite-difference discretisation in physical space, and a Hermite function expansion in velocity space. Numerical convergence errors in the Fokker-Planck equation solutions are shown to be much less than the statistical error associated with a practical-sized ensemble (N = 106) of LPDM solutions, hence the former can be used to validate the latter. The test problems are then used to evaluate commonly used LPDM integration schemes. The results allow for optimal time-step selection for each scheme, given a required level of accuracy. The following recommendations are made for use in operational models. First, if computational constraints require the use of moderate to long time steps it is more accurate to solve the random displacement model approximation to the LPDM, rather than use existing schemes designed for long time-steps. Second, useful gains in numerical accuracy can be obtained, at moderate additional computational cost, by using the relatively simple "small-noise" scheme of Honeycutt.

Experimental Evaluation of a Hermite Function-Based Multicarrier Scheme for VLC

2021 ◽  
Author(s):  
Carlos Guerra-Yanez ◽  
Stanislav Zvanovec ◽  
Zabih Ghassemlooy
Keyword(s):  
Experimental Evaluation ◽  
Hermite Function

scholarly journals Voriconazole versus Itraconazole for the Initial and Step-Down Treatment of Histoplasmosis: A Retrospective Cohort

2020 ◽  
Author(s):  
Michael Joshua Hendrix ◽  
Lindsey Larson ◽  
Adriana M Rauseo ◽  
Sasinuch Rutjanawech ◽  
Alexander D Franklin ◽  
...  
Keyword(s):  
Retrospective Cohort ◽  
Proportional Hazards ◽  
Histoplasma Capsulatum ◽  
Case Reports ◽  
Case Series ◽  
Clinical Information ◽  
Cox Proportional Hazards ◽  
Heaviside Function ◽  
Step Down

Abstract Background Itraconazole is the preferred azole for histoplasmosis in the current Infectious Diseases Society of America guidelines. Voriconazole is increasingly used as treatment for histoplasmosis; it has in-vitro activity against Histoplasma capsulatum and has shown success in case reports and small case series but may have a lower barrier to resistance. No comparative studies have been published. Methods We constructed a single-center retrospective cohort of adult patients diagnosed with histoplasmosis from 2002 to 2017. Individual charts were reviewed to gather clinical information including demographics, clinical features, immune status, treatments, and mortality. Patients were categorized based on initial choice of azole, either as initial treatment or as step-down therapy from amphotericin B. Initial therapies with other azoles were excluded. Mortality was compared using a multivariable Cox proportional hazards with Heaviside function at 42 days. Results We identified 261 cases of histoplasmosis from 2002 to 2017. After excluding patients not treated with itraconazole or voriconazole, 194 patients remained. 175 (90%) patients received itraconazole and 19 (10%) received voriconazole. There were no significant demographic differences between patient populations receiving either azole as their initial azole treatment. Death at 180 days occurred in 41 patients (23.4%) in the itraconazole group and 6 patients (31.6%) in the voriconazole group. Patients on voriconazole had a statistically significant increase in mortality during the first 42 days after initiation of treatment when compared to patients receiving itraconazole (HR 4.30 [95% CI 1.3-13.9, p 0.015]) when controlled for other risk factors. Conclusion Voriconazole in histoplasmosis was associated with increased mortality in the first 42 days compared to itraconazole.

XFEM with partial Heaviside function enrichment for fracture analysis

2021 ◽  
Vol 241 ◽  
pp. 107375
Author(s):  
Y. Jiang ◽  
J. Dong ◽  
D.F. Nie ◽  
X.Q. Zhang
Keyword(s):  
Fracture Analysis ◽  
Heaviside Function ◽  
Function Enrichment
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