C#
#Programming #Physics #Unity3D
In this project, we modeled the Solar system based on real celestial mechanics. A system of ordinary differential equations is solved numerically with the actual positions and velocities of space bodies at January 1st, 1978 taken as the initial conditions. This application provides flexible control of the camera to observe the Sun, planets and satellites from different points, allowing you to watch this amazing physical process that is otherwise inaccessible to the human eye. It is possible to switch the observer’s location between space bodies and see, for example, a sunrise on Mars. The standard 3D camera operations like rotation, panning, zooming etc. are supported.
The Sun and the planets are very small in comparison with the distances between them. As a result, the observer located on Pluto sees the Sun as just one of billions of other stars. Observation of the whole Solar system in quantitatively exact proportions does not provide a clear qualitative picture. This is why we provided a panorama mode in this application so that the user can watch the bodies in a much bigger size and closer to each other than they are in real life.
The user is also able to throw in new celestial bodies and see the resulting changes in the evolution of the Solar system.
The core of the application is a dynamiclink library that calculates motion trajectories based on real physics. The 3D graphical user interface was implemented for Windows, Android and Web platforms with Unity. A simple 2D graphical user interface was implemented as well. It was developed as a prototype and used for testing of the core library.
https://vimeo.com/148773041

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C#
#Programming #Physics
In vino veritas, in aqua sanitas.
This project was devoted to fluid mechanics modeling with OpenFOAM library being an extremely powerful open source toolbox with a broad set of solvers mainly designed for computational fluid dynamics.
Both preparation of the input data and visualization of the output data are nontrivial for this library, requiring some expertise in working with it. The application we developed facilitates the interface between end user and OpenFOAM making it easy to formulate a problem, conduct simulation and analyze its results. With a friendly GUI, the user can adjust spatial and temporal grids, set initial distribution of fluid in tank and start the finitedifference timedomain process with just one mouse click. The results of simulation are automatically loaded, postprocessed and shown to the user in the form of an animation. Optionally, they can be saved to a video file with AVI extension.
The initial geometry of fluid can be drawn by the user just like in a common graphics editor, using an adjustable brush. It is possible save the geometry and to load it later in order to conduct simulations with other fluid properties, e.g. density or viscosity.
https://vimeo.com/157211549

5
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Application programming
#Programming #Matlab #Mathematics
This application is for the exploration of the impact of economic data releases on the foreign exchange market. It is a tool that combines three kinds of data collected from different sources and presents them together in a userfriendly form:
1. Foreign exchange rates are imported from the most popular trading platform MetaTrader4.
2. The information of major economic data releases is imported from the ForexFactory calendar.
3. Dow Jones Newswires news feed.
The primary customer is a Forex trader who wants to verify the effectiveness of various trading strategies applied at the moment of major economic data releases.
With this application, user can, for example, find all releases of US Nonfarm Payrolls where the difference between the actual released value and the forecasted value was greater than a given threshold. Thereafter they can see how the exchange rate of US dollar to Japanese yen (or other currency pair) was affected by these releases in 1minute, 5minutes and 15minutes time frames.
Simultaneous releases and durable news (e.g. speech of Fed Chairman Ben Bernanke) are indicated on the candlestick chart gracefully. News of different countries are shown with labels of different color for visual convenience.

8
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C#
#Programming #Physics
A finitedifference timedomain method that is used to integrate the wave equation of a given rectangular area where permittivity function and sources function are defined.
The input of the application is a BMP file where red and green regions denote low and high permittivity values respectively, black pixels define opaque area, and magenta pixels specify the locations of harmonic sources.
Output is an AVI file with a cool video showing the propagation of electromagnetic waves through the media.
https://vimeo.com/145061117

1
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C#
#Mathematics #Programming
Have you ever dived into the beautiful world of fractal art?
The Mandelbrot set is defined by an extremely simple recurrent equation, but its magic images make our hearts beat faster.
This application generates an AVI file with Mandelbrot set zooming video. The user is able to change the zoom target point by clicking the image at any moment in the process.
https://vimeo.com/145060877

3
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Application programming
#Fortran #Physics
Microstrip is a type of electrical transmission line that can be fabricated using printed circuit board technology. It is used to convey microwavefrequency signals.
This application allows the user to calculate the electrical properties of a microstrip line in a given geometry produced from set materials (analysis), or to determine the geometry necessary to obey the given requirements for an impedance (synthesis).
This application not only calculates the value of a parameter, but also shows the dependence of that value versus frequency, width of the conductor, or height of the dielectric substrate.

2
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C#
#Programming #DataProcessing
Volnozor is an application that represents by itself the basis for studying the fine, detailed threedimensional and twodimensional images of waves of different nature, as well as interactions with them.
Each threedimensional image consists of several layers for convenient handling. Any of those layers can be switched on and off. There are all necessary possibilities for changing the position of the image and the angle of view by the user. There is also taken into account the peculiarities of the reflection of waves with different natures, according to human perception.
The idea embodied in the structure of this application allows it to fill its functionality by different kinds of waves, and to reflect the characteristics in its visual presentation. There is also the possibility to complement the exploratory and modify data toolkit. Also provided are the reading and writing of the images from storage or stream.

1
0


Application programming
#Physics #Matlab #Mathematics
This software calculates electric field impulse reflection response (IRR) in a given multilayered dielectric sample.
The initial excitation is a Dirac impulse falling from semiinfinite media to the frontal surface of the sample. The impulse propagates inside the sample, and undergoes both reflection and transmission on each interface between two adjacent layers. As a result, the number of secondary impulses raises in geometrical progression.
The goal of this simulation is to calculate the IRR of a given time interval. The IRR is defined by two equal length vectors describing impulses leaving the sample in the direction opposite to the initial excitation:
1. The vector of time delays.
2. The vector of magnitudes.
User can select whether to obtain the main reflections only or to take into scope all the reverberations in a given time interval. Both flat and diverging fronts are supported for the irradiating impulse. Special facilities are implemented for correct handling of the samples where the layers have divisible electrical depths.

3
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Application programming
#Physics #Matlab #Mathematics
This software provides the first step in a simulation where nondestructive testing of dielectric samples is modeled. It calculates the reflection coefficient of multilayered dielectric samples in a wide frequency band. The geometry of the sample, the properties of its dielectric layers, and the frequency grid and noise are specified by the user. The output data can be passed for further processing in order to extract the characteristics of the original sample based on its reflection coefficient.

3
0


Application programming
#DataProcessing #Physics #Matlab #Mathematics
This software was designed as a processor of microwave reflectometer raw output data. The reflectometer measures the power of the reflected wave of a given sample in a wide frequency band. It provides the extraction of a complexvalued reflection coefficient from absolutevalued data utilizing the Fourier holography concept. This concept brings the following algorithm of data processing:
1. Measure the power reflection coefficient of a given sample under investigation.
2. Measure the power reflection coefficient of a given metal sheet placed at the same distance from the horn as the sample frontal plane.
3. Transform both characteristics from the frequency domain to the time domain with discrete Fourier transform.
4. Apply a weight window to the signal suppressing artifacts of reflection from horn throat and aperture, fastening tools, and other objects present in the laboratory.
5. Transform both characteristics from the time domain to the frequency domain and divide one to the other. The complexvalued reflection coefficient is obtained as a result.

2
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Application programming
#Algorithm #DataProcessing #Mathematics #Matlab
This software takes a sampled signal in a frequency domain and performs a spectral analysis based on the rational interpolation in Fourierconjugate time domain. The assumed model of the analyzed signal versus frequency is a sum of complexvalued exponential terms with unknown magnitudes and phases. The goal is a determination of the unknown parameters.
The method is grounded on the fact that such a model corresponds to the sum of pole functions in the time domain. This efficient method of poles parameters extraction is an interpolation of the sampled spectrum with a chain fraction where the interpolation points selected in maximums of the residual spectrum. This interpolation yields zeros and poles that are converted to the magnitudes and phases of the exponents.

2
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Application programming
#DataProcessing #Physics #Matlab #Mathematics #Algorithm
This software provides the reconstruction of the permittivity profile of a multilayered dielectric sample based on microwave reflectometry data acquired in a wide frequency band. The modified NewtonKantorovich iterative scheme is implemented.

1
0


Application programming
#Mathematics #Statistics #Matlab
This software calculates CramerRao boundaries (i.e. minimum achievable values) for the variances of multilayered structures parameters estimates obtained as a result of the spectral analysis of microwave reflectometry data. The boundaries are shown in the form of colormaps depending on the true position of a pole relative to the interpolation points.

1
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Application programming
#Physics #Matlab #Mathematics
The influence of various types of distortion of periodicity on the eigen parameters of the layered Bragg resonators is analyzed. The conditions for the reduction of the quality factor of unwanted side Bragg oscillations in quasiperiodic apodized resonators is determined. It proposes the construction of periodic and quasiperiodic structures and apodized Bragg resonators with thin contrast layers, which are relatively easy to technologically implement in the microwave range.
The perturbation of the parameter of periodical Bragg structure is a flexible tool to obtain the desired reflection and transmission characteristics. Apodization of Bragg reflectors leads to a significant reduction of side lobes, while the main maximum is expanding, and its amplitude decreases slightly.
The minimum level of the first sidelobe can be obtained when the apodized function is as smooth as possible. The influence of apodization on the eigenfrequencies of structure increases with growing the distance between the frequency of the Bragg reflections and eigenfrequency. With the introduction of the violation of the structure periodicity as a double thickness of the central layer, there are conditions for the appearance of a high quality oscillation in the Bragg reflection band. Under the apodization of Bragg resonators the frequency selectivity increases due to the relative decrease of the resonances quality factor for the side resonance frequencies subject to the condition that an average contrast throughout the thickness of the structure saves its value.

1
0


Application programming
#Matlab #Physics #Mathematics
The time delay, space shift and widening of wave packet transmitted and reflected by structures with Bragg mirrors is investigated. The specific structures such as Bragg mirrors, resonators, and structures with chirp variation of thickness of the “period” are also considered. The calculation is carried out under the conditions that carrier frequency and incidence angle are in the vicinity of the Bragg resonance. Integral (mass center) and differential (group) estimates of the delay time and space shift are then compared. The conditions for the appearance of anomalous (negative) mass center delay or mass center shift (GoosHänchen shift) of the reflected wave packet are determined. The shape transformations of the wave packet illuminating periodic and quasiperiodic apodized Bragg reflectors are then considered. Spatial apodization of permittivity contrast yields a much smaller shape deformation of the transmitted wave packet upon incidence at angles and carrier frequency near the edges of the reflection band, as well in the Bragg reflection band, in comparison with phenomena in similar periodic structures. The values of group delay for layered structures with a small chirp variation of optical (electrical) thickness of the period along longitudinal coordinates is experimentally obtained in the microwave range.
GD and GS packet negative values are inherent to asymmetric Bragg resonators and observed under the condition that a resonance thickness layer is located closer to the end of a structure. In the case of large wave packet durations and extent, integral and deferential packet estimates take approximately equal values. CMD and CMS have anomalous values via packet distortions: widening, variation of asymmetry, coefficient of kurtosis.

1
0


Application programming
#Matlab #Physics #Mathematics
The behavior of quasiperiodic and nonperiodic (chirp) Bragg structures with thin lossy layers is considered. In order to calculate the dependence of the reflection coefficient against frequency, the transmission matrix method was used. A deep minimum of reflection coefficient for any frequency is implemented by properly choosing the thickness of the last thin film and its optical distance to the substrate. The possibility of providing broadband reflection by nonperiodic structures is offered.
Quasiperiodic Bragg structures with thin lossy layers can operate as good absorbers in a given frequency band. Variation of the conductivity of a lump inhomogeneity is obtained by varying the thickness of a thin lossy layer. For a fixed frequency, minimum reflectivity can be provided by the choice of the parameters of layer thickness and the distance to the substrate. Broadband absorption is achieved by nonuniform perturbation of optical thickness of the separating dielectric layer.

1
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Application programming
#Matlab #Physics #Mathematics
One of the most important technical applications of nonlinear material properties is to create logical devices, memory devices and data processing devices based on the hysteresis phenomenon. An actual problem for the development of modern information technology is the realization of such devices in the terahertz frequency range, and to increase performance while reducing size and weight.
Using the Bragg reflectors for strong frequencyselective feedback in FabryPerot resonator allows us to observe multistability with less thickness of the nonlinear layer. In most cases, the exact solution of the problem of electromagnetic field distribution on the boundary of the layered Bragg structure with Kerr nonlinear layers can not be found, and we have to use approximate numerical methods.
The proposed method allows us to investigate the resonance properties of structures with different combinations of nonlinear layers, including Bragg structures containing layers with several types of Kerr nonlinearity. The choosing of inclusion points of lumped nonlinear elements is a flexible tool to achieve the desired multistable frequency and amplitude characteristics.

3
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Application programming
#Matlab #Physics #Mathematics
The methods of piecewise constant and piecewise linear approximation of complicated inhomogeneous layers are investigated. The expressions for transmission matrices for linearly inhomogeneous and exponentially inhomogeneous layers are obtained. The accurate and approximate values of reflection coefficient against frequency for the exponential and linear matching layers is also obtained. Piecewise constant and piecewise linear approximation methods are compared according to the criteria of calculating time consumption and the accuracy of the result.
These methods allow us to obtain approximate values for the reflection coefficient of complex heterogeneous layers. The piecewise linear approximation method is more suitable in a case where the permittivity is a rapidly varying nonmonotonic function. If the number of layers is increasing, the error of the reflection coefficient for the piecewise linear approximation decreases faster than that for the piecewise constant approximation. With increasing frequency, the error of piecewise linear and piecewise constant approximation increases. An equal number of layers, the error of piecewise linear method is lower than the error of piecewise constant for all of the frequency range.

1
0


C/C++
#DigitalFilterDesign, #IIR, #DSP
The goal of this project was the implementation of a full analogue of iirlpnorm Matlab function being a part of DSP System Toolbox. The function is for the synthesis of Infinite Impulse Response (IIR) digital filter with piecewiselinear amplitude response using leastweightedPth approximation. It is not an opensource function in contrast to many other Matlab functions.
A quasiNewton minimizer in couple with a simplex line searcher are employed in the heart of our program. Since the objective function is very jagged, it was decided to use a twostage optimization strategy with two objective functions minimized in sequence. The first objective function being a rough approximation of the second (true) objective function has a virtue of smoothness. It allows us to obtain a good initial estimate for the second stage of optimization.
The program was implemented in C++ with the usage of Intel® Math Kernel Library for polynomial roots finding. (The roots are found as eigenvalues of the associated companion matrix.)
The original Matlab function does not allow watching the convergence process. However, we provided such possibility in our function through intermediate data dumping mechanism. The process is shown in the next video for several test cases. We used Matlab with its rich visualization functionality for the preparation this video.
In general case, ideal fitting of a piecewiselinear amplitude response can be accomplished only with an IIR filter of infinite order. Despite this, we used a model with only 10 zeros and 15 poles in all the tests. Also, we used the same initial estimate shown at start of the video.
Implementation of the twostage optimization strategy allowed us to achieve convergence in some cases where the original Matlab function didn’t find the solution (e.g. in Test 3 shown in the video).
https://vimeo.com/150297951

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