Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

A weighted group shuffled decoding for low-density parity-check codes

In this paper, we have developed several concepts such as the tree concept, the short cycle concept and the group shuffling concept of a propagation cycle to decrypt low-density parity-check (LDPC) codes. Thus, we proposed an algorithm based on group shuffling propagation where the probability of occurrence takes exponential form exponential factor appearance probability belief propagation-group shuffled belief propagation (EFAP-GSBP). This algorithm is used for wireless communication applications by providing improved decryption performance with low latency. To demonstrate the effectiveness of our suggested technique EFAP-GSBP, we ran numerous simulations that demonstrated that our algorithm is superior to the traditional BP/GSBP algorithm for decrypting LPDC codes in both regular and non-regular forms

Why Time Discounting Should Be Exponential: A Reply to Callender

According to Craig Callender (2020), the “received view” across the social sciences is that, when it comes to time and preference, only exponential time discounting is rational. Callender argues that this view is false, even pernicious. Here I endorse what I take to be Callender’s main argument, but only insofar as the received view is understood in a particular way. I go on to propose a different way of understanding the received view that makes it true. In short: When time discounting is suitably conceived, the exponential form of the discounting function is indeed uniquely rational.

Cosmic inflation in some viable modified models of f(R) gravity of polynomial-exponential form

In this paper, we present the cosmic inflation scenario in some viable models of the f(R) modified gravity of polynomial-exponential form. Results show that the magnitude of the parameter β in these viable models is at the order of 5.67x10–76 and the time of inflation is at the order of 4.6 x 10–35 s.

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.

Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to developments of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model as the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and polynomial forms (R2=0.92-0.99 vs. 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 vs. 0.30), indicating a more well-defined search space. Finally, the exponential and combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential SEDF leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets due to its superb fitting capabilities and smaller parameter's confidence regions.

Note on the Charged Black Hole Solutions in a Static Quantum Inspired Spacetime: Massive Gravity as Background

In this paper, we explore the black hole solutions with rainbow deformed metric in the presence of exponential form of nonlinear electrodynamics with asymptotic Reissner-Nordstrom properties. We calculate the exact solution of metric function and explore the geometrical prop- erties in the background of massive gravity. From the obtained solution, the existence of the singularity is confirmed in proper limits. Using the solutions we also investigate the thermody- namic properties of the solutions by checking the validity of the first law of thermodynamics. Continuing the thermodynamic study, we investigate the conditions under which the system is thermally stable from the heat capacity and the Gibbs free energy. We also discuss the possible phase transition and the criticality of the system. It was found that the quantum gravitational effects of gravity’s rainbow render the thermodynamic system stable in the vicinity of the singu- larity. From the equation of state it was found that after diverging at the singularity, the system evolves asymptotically into pressure-less dust as one moves away from the central singularity.

Study the influences of the radionuclide depth distributions on the FEPE for the measurements of the soil activity using in situ HPGe gamma spectrometry

In this work, the influences of the soil densities and the radionuclide depth distributions(RDD) on the Full Energy Peak Efficiency (FEPE) calculation of the in-situ gamma rayspectrometer using the In Situ Object Counting Systems (ISOCS) software were studied. The data of the RDDs at the sites were investigated by using laboratory HPGe gamma spectrometer. Six different RDDs of 40K, 226Ra and 232Th were found at four studied sites with radionuclide deposition moving from surface to deeper positions. The results show that FEPE values vary strongly for the different RDDs, especially for the low gamma ray energies. Use of the uniform model for calculating FEPEs can result in noticeable errors from 29% to 101% for the realistic RDD of the exponential form (surfaceradionuclide deposition), negative variations from 14% to 30% for the realistic RDD of having a radionuclide deposition at the 30 cm depth, and negligible variations of less than 5 % for the realistic RDD of quasi uniform form in the range of gamma ray energies of interest.

New Orthogonal Transforms for Signal and Image Processing

In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having an exponential form is also presented. Orthogonal basis functions based on the created matrices can be used for orthogonal expansion leading to signal approximation. An exponential form of orthogonal, sparse matrices with variable parameters is also created. Various versions of orthogonal transforms related to the created full and sparse matrices are proposed. Fast computation of the presented transforms in comparison to fast algorithms of selected orthogonal transforms is discussed. Possible applications for signal approximation and examples of image spectrum in the considered transform domains are presented.

Generalized Analysis of Division Algebras of Dimension 2

The mathematical properties of division algebras of dimension 2 are investigated on the basis of the analysis of possible values of the parameters introduced into the laws of composition of basic elements. Generalized expressions for calculating the inverse and neutral elements of the indicated algebras are given. The relations of the parameters defining the normalized division algebras are determined. Possibilities of application of linear orthogonal transformations for the analysis of isomorphism of such algebras are considered. The concept of an exponential function is introduced to represent the elements of the considered non-commutative division algebra in exponential form.