A one-dimensional two-zone mathematical model, comprising a pair of advection-dispersion equations coupled by a mass exchange term, is proposed to study longitudinal dispersion in channels with sequences of pools and riffles. An implicit finite-difference numerical scheme is employed, and its effectiveness is assessed with reference to known analytical solutions. Moreover, sets of longitudinal dispersion experiments were performed on various simple geometries of sequences of pools and riffles developed in a laboratory flume. The results were compared with corresponding numerical solutions to calibrate the two-zone model. and Pro studium podélné disperze v korytech s opakující se soustavou tůní a prahů byl navržen jednorozměrný dvouzónový matematický model. Model zahrnuje dvojici rovnic pro advektivní disperzi doplněných výrazem pro přenos hmoty. Byl použit implicitní model konečných diferencí a jeho vhodnost ověřena porovnáním se známým analytickým řešením. Navíc, v laboratorním žlabu byla provedena série měření podélné disperze pro různé jednoduché geometrie koryta se střídajícími se tůněmi a prahy. Pro kalibraci dvouzónového modelu byly výsledky měření porovnány s odpovídajícími matematickými řešeními.
In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).
Various population indices are widely used to monitor relative population size of many pest and game species to aid their management. However, information on the level of uncertainty associated with their estimates is rarely available. Here we explore sampling and systematic error associated with the index of re-opened burrow entrances which is used extensively in central Europe for surveying common vole populations. We found that relative sampling errors were enormous for low-density populations, attaining almost 400%. However, in high-density populations and for large sample sizes, the relative error dropped below 10% and the estimate is quite reliable. The dispersion of burrow entrances became more clumped at low population densities enhancing further the sampling variation. We demonstrated that the index is related to population size in a non-linear fashion, overestimating the population change at high densities. Consequently, population dynamics of the common vole described by the untransformed burrow index appear more variable than they are in reality.
The results of wide spectral range dispersion measurement of a twomode birefringent microstructured fibre are presented. A spectral interferometric method using a tandem configuration of a Michelson interferometer and a fibre under test is performed. The group modal birefringence dispersion for two linearly polarized modes supported by the fibre is examined. The measured values are fitted to polynomials to obtain the dispersion of the phase modal birefringence for both modes. it is shown that the results correspond to the approximation of the phase modal birefringence of the fundamental mode in air-silica fibres. and V příspěvku jsou prezentovány výsledky měření disperze dvouvidového dvojlomného mikrostrukturního optického vlákna (DMOV) v širokém spektrálním oboru. Nejprve je spektrální interferenční metodou, využívající tandemového uspořádání Michelsonova interferometru a testovaného vlákna, zjišťována disperze skupinového dvojlomu pro dva lineárně polarizované vidy vedené DMOV. Naměřené hodnoty jsou proloženy polynomy tak, aby byla získána disperze fázového dvojlomu pro oba vidy. Je ukázáno, že výsledky měření se shodují s aproximací fázového dvojlomu základního vidu, která je vhodná pro křemenné DMOV se vzduchovými otvory.
In the present work, existing empirical expressions for longitudinal dispersion coefficient of rivers (K) are evaluated. They are found inadequate primarily because these expressions ignore the channel sinuosity, an important parameter representing a river’s transverse irregularities that affect mixing process. Hence, a new expression for K is derived taking into account the sinuosity besides few of other hydraulic and geometric characteristics of a river. The model makes use of genetic algorithm (GA) on published field data. Based on several performance indices, the new expression is found superior to many existing expressions for estimating K. The sensitivity and error analysis conducted on parameters of the new expression show the channel sinuosity an important input for predicting K accurately. Any error in measurement of sinuosity would lead to significant deviation in the longitudinal dispersion coefficient in sinuous rivers.
All phenomena in nature are going on continuity way. All independent and dependent quantities are changing with time. Solving the problems of advection and dispersion of an observed component in a system of river network, influences of time and dispersion cannot be neglected in general. Since knowledge of hydraulic quantities (average velocity and cross sectional area) are presumed, a concentration c(x,t) of the observed component in a stream is the only unknown function. To determine this function c(x, t), one equation is needed - Advective-Dispersion Equation (ADE). ADE expresses law of mass conservation. The paper deals with analytical solutions of problems of transport and dispersion of the observed component in streams, namely for steady and unsteady problems. Analytical solutions are useful for validation of numerical solutions and for sensitivity analysis. The sensitivity analysis helps to determine influences of a separate coefficient of a model. Analytical solutions are derived dfor constant velocity, constant discharge and constant cross-sectional area. Also it is assumed constant dispersion coefficient. and V přírodě probíhají všechny jevy kontinuálně, kdy veškeré nezávislé, ale i závislé veličiny se mění s časem. Při řešení úloh transportu a disperze látky v systému vodotečí se obecně nemůže zanedbat vliv času a účinku disperze. Jelikož se předpokládá znalost hydraulických veličin proudění vody v toku (rychlost a průtočná plocha), je jedinou neznámou funkcí koncentrace látky v toku c(x, t). K jejímu určení je zapotřebí jedna rovnice (rovnice transportu a disperze), která se získá aplikací zákona zachování hmotnosti. Předmětem článku jsou analytická řešení rovnice transportu a disperze látek v tocích, a to jak pro stacionární tak nestacionární děje. Analytická řešení jsou vhodná pro ověření přesnosti numerických řešení a pro citlivostní analýzu, pomocí které je možné určit vliv jednotlivých koeficientu modelu. Analytická řešení jsou odvozena pro konstantní průřezovou rychlost, konstantní průtok a konstantní průtočnou plochu, tedy pro rovnoměrné ustálené proudění. Dále se předpokládá konstantní součinitel disperze na celém studovaném úseku toku (oblasti řešení).
Rayleigh waves in the period range 0.2 - 3.0 s from eight quarry blasts are analyzed to obtain S-wave velocity model beneath the Příbram seven-station array in the Czech Republic. Locations and origin times of blasts are estimated using P- and S-wave onsets and then verified at the quarry in the vicinity of the location. This blind test confirms a sufficient precision of the location procedure for identification of quarries. Epicentral distances are in the range from 16 to 52 km. Group velocity dispersion curves of Rayleigh waves are determined by the frequency-time analysis. An average group velocity beneath the array for each period is computed with the help of mean travel-time curve for all blasts and stations. The resultant group velocity dispersion curve is inverted to obtain a 1-D S-wave velocity model using the Isometric method. The results are compared with known geological structure in the area of interest., Renata Gaždová, Petr Kolínský, Jiří Málek and Jan Vilhelm., and Obsahuje bibliografii
This paper presents the effect of various reflectance models of the thin-film structure system on determination of the thin-film thickness. A special program was created in software package Matlab, which is able to calculate theoretical spectral reflectance in selected wavelength interval for the certain thin-film thickness. Afterwards, this reflectance, which simulates experimental reflectance during the following study, is processed by other program in Matlab. In this way the simulated reflectance is fitted to theoretical one with thin-film thickness as fitted parameter. Different combinations of optical parameters - dispersive and non-dispersive - for the thin-film structure system can be used as the input for the program files in the fitted reflection spectrum. Finally, the effect of reflectance models on the value of the thin-film thickness is discussed. and Práce prezentuje vliv použití různých modelů odrazivosti systému tenká vrstva - podložka na vypočtení tloušťky tenké vrstvy. V prostředí Matlabu je vytvořen program, který pomocí obecného modelu vypočte teoretický průběh spektrální odrazivosti v závislosti na vlnové délce pro zvolenou tloušťku tenké vrstvy. Takto vypočtená odrazivost, která v další fázi studia simuluje naměřenou odrazivost, je zpracována dalším programem v Matlabu, který simulované (naměřené) reflexní spektrum fituje spektrem teoretickým, kde fitovaným parametrem je tloušťka vrstvy. Ve vstupních souborech fitovaného teoretického reflexního spektra jsou použity různé kombinace disperzních a nedisperzních optických parametrů systému tenká vrstva - podložka a je sledován jejich vliv na hodnotu vypočtené tloušťky tenké vrstvy.
By the selection of materials for optical systems in infrared (IR) region of electromagnetic waves is important to consider their physical properties and spectral area of use. When designing IR optical systems often occurs the problem that some physical parameters of materials were not taken into account, causing the error, and difficulties for their application. In this paper we try draw attention to these problems. and Pri výbere materiálov pre optické systémy v infračervenej (IR) oblasti elektromagnetických vĺn je dôležité zohľadniť ich fyzikálne vlastnosti a oblasť ich použitia. Pri navrhovaní IR optických systémov sa často vyskytuje problém, že niektoré fyzikálne parametre materiálov nie sú zohľadňované, čo spôsobuje chyby a problémy pri ich aplikácii. V príspevku sa snažíme upozorniť na tieto problémy.