Small Values Of Parameter Research Articles

Design of power control system for automatic operation of the Kartini reactor

Kartini research reactor which is located at Yogyakarta Indonesia is intended for research, education and training. Students from universities around the city use the reactor for experiments regularly. Regarding the plan of building the first nuclear power plant in Indonesia, the reactor could be improved as the facility of a nuclear power simulator for personnel training of a nuclear power plant. Some improvements on instrumentation and control system were conducted to support the purpose, such as developments of data acquisition of reactor operation parameters, and internet reactor laboratory for remote experiment through the internet connection. However, a power control system for the automatic operation of the reactor is not developed yet. It is important to design an automatic power control for the improvement of the reactor as a simulator of a light-water nuclear power plant. This paper discusses the design of power control of the Kartini reactor based on the Kartini reactor accident and transient code. The control model refers to that of a light water-cooled nuclear power plant. Calculation results show that the control model is applicable to the Kartini reactor. The criterion of SCRAM actuation of the Kartini reactor is satisfied by a small value (0.1) of a control parameter of b. In the future, the control rod simulator which is available in the Kartini reactor might be used to simulate the control system before it is realized to the real reactor.

Stability analysis by averaging: a time-delay approach

We study stability of linear systems with fast time-varying coefficients. The classical averaging method guarantees the stability of such systems for small enough values of parameter provided the corresponding averaged system is stable. However, it is difficult to find an upper bound on the small parameter by using classical tools for asymptotic analysis. In this paper we introduce an efficient constructive method for finding an upper bound on the value of the small parameter that guarantees a desired exponential decay rate. We transform the system to a model with time-delays of the length of the small parameter. The resulting time-delay system is a perturbation of the averaged LTI system which is assumed to be exponentially stable. The stability of the time-delay system guarantees the stability of the original one. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on the small parameter that preserves the exponential stability is found from LMIs. Two numerical examples (stabilization by vibrational control and by time-dependent switching) illustrate the efficiency of the method.

Mean-Variance Portfolio Selection with Tracking Error Penalization

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by “fitting” it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Mathematical modeling of forest fire extinguishing using water capsules with a thermoactive shell

The paper proposes a new mathematical model of the process of extinguishing a forest fire with dispersed water delivered to the fire source with water capsules with a thermoactive shell. When moving in a medium with a temperature above the critical, the capsule shell accumulates the integral value of the damage with the intensity proportional to the distance traveled and the critical temperature exceed. When the integral parameter of the thermal stability of the shell is reached, the capsule ruptures and water is released in dispersed form. During the sequential discharge of several capsules, each of them is affected by the temperature of the medium formed after exposure to the previous capsules. After calculating the distribution of dispersed water from the capsules, the calculation of the dynamics of a forest fire based on a physical and mathematical model is resumed. The analysis of key parameters and effects that determine the effectiveness of extinguishing is carried out. The extinguishing dynamics is shown for a different number of capsules per unit length of the fire front, an integral parameter of thermal stability, and the amount of water in the capsule. The results of numerical modeling showed that in the case of a small value of the capsule integral parameter of thermal stability, the capsule ruptures in the upper part of the vegetation layer, and therefore a great number of water capsules must be sequentially dumped to extinguish. Too high value of the thermal stability coefficient leads to rupture of capsules on the ground and to continuation of the combustion process in the upper part of the vegetation layer. The greatest efficiency of forest fire extinguishing occurs when the thermoactive shell of capsules ruptures in the middle of the combustion front. Sequential discharge of capsules allows one to distribute water vertically, more fully covering the zone of vulnerability of the fire. It is shown that the use of capsules with a thermoactive shell allows one to deliver water in the zone of vulnerability of the fire, thereby providing more effective firefighting.

Analysis of relaxation of varistor-posistor voltage limiting device in photovoltaic modules during renewal of lighting

The features of the operation of the circuit method based on a structure of a varistor-PPTC fuse type being in thermal contact to protect the photovoltaic cells from overvoltages arising from the partial shading of the photovoltaic modules of solar arrays are considered. The conditions for the relaxation of the functional characteristics of such voltage limiting devices to the initial state which does not affect the operation of the photovoltaic module during renewal of lighting of the photovoltaic cells are analyzed. It is established that the temperature and resistance dependences of the PPTC element, which determine its state, have a relaxation character at small values of such parameters of the voltage limiting device as the passport values of the resistance of the PPTC element in the conducting (“cold”) state and thermal resistance of the voltage limiting device. The relaxation time is of the order of a few seconds. For large values of the indicated parameters, a situation may occur when such relaxation is absent and the voltage limiting device maintains an active low-conductive (“hot”) state.

Influence of Density Dependence of Symmetry Energy in Hot and Dense Matter for Supernova Simulations

Abstract We study the influence of density-dependent symmetry energy at high densities in simulations of core-collapse supernovae, black hole formation, and proto–neutron star cooling by extending the relativistic mean field (RMF) theory used for the Shen equation-of-state (EOS) table. We adopt the extended RMF theory to examine the density dependence of the symmetry energy with a small value of the slope parameter L, while the original properties of the symmetric nuclear matter are unchanged. In order to assess matter effects at high densities, we perform numerical simulations of gravitational collapse of massive stars adopting the EOS table at high densities beyond 1014 g cm−3 with the small L value, which is in accord with the experimental and observational constraints, and compare them with the results obtained by using the Shen EOS. Numerical results for 11.2 and 15 M ⊙ stars exhibit minor effects around the core bounce and in the following evolution for 200 ms. Numerical results for 40 and 50 M ⊙ stars reveal a shorter duration toward the black hole formation with a smaller maximum mass for the small-L case. Numerical simulations of proto–neutron star cooling over 10 s through neutrino emissions demonstrate increasing effects of the symmetry energy at high densities. Neutrino cooling drastically proceeds in a relatively long timescale with high luminosities and average energies with the small symmetry energy. Evolution toward the cold neutron star is affected because of the different behavior of neutron-rich matter, while supernova dynamics around core bounce remains similar in less neutron-rich environments.

A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction–convection–diffusion systems with two small parameters and discontinuous source terms

This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction–convection–diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.

Differential Transform Technique on the Effect of Baffle Convective Nanofluid Flow in Saturated Porous Channel

Simulations are shown for steady nanofluid saturated with porous medium in a vertical channel divided into two way by placing a thin baffle. Tiwari and Das model applied for continuity, momentum and energy equations are written using to define the nanofluid and non-Darcy model used for porous medium. The nonlinear equations are solved analytically using regular perturbation method and by semi analytical method using differential transform method. The validity of the solutions obtained by perturbation method and differential transform method are compared and found that they agree very well for small values of perturbation parameters. The numerical values of the velocity and temperature are shown graphically at different baffle positions for all the pertinent parameters. The Nusselt number for both regular and nanofluids are evaluated and tabulated.

Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model

Thermoelastic damping (TED) is considered to be a factor of significant energy loss in micro-scale structures, even at room temperature. The prediction of TED is therefore very important in the designing of micro-electro-mechanical system (MEMS) resonators with high-quality factors. When the thickness of the beams and plates are at microscale or nanoscale, the size-effect is needed to be considered. Couple stress theory is developed as a size-dependent continuum theory to deal with such problems. In the present work, an analytical expression for the quality factor (Q) of TED for size-dependent microplate resonators is derived by applying the modified couple stress theory (MCST) considering plane stress condition and the three-phase-lag (TPL) heat conduction model. We consider Kirchhoff microplate resonators and as case study, the effect of the length-scale parameter on the quality factor of TED are discussed in detail. To study the behavior of TED, the material of the microplate resonator is considered to be Silicon. The variations of TED as functions of the normalized frequency, microplate thickness, and length-scale parameter have been investigated. The effect of phase-lag parameters on TED has also been discussed. The results of the present model are compared to the existing results of the classical continuum theory. The present work investigates that the modified couple stress theory with small values of phase-lag parameters can increase the quality factor of microplate resonators with a smaller thickness.

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko’s, Vogel’s, and Agarwal–Tara’s criteria as well as the criteria of lower- and higher-order antibunching, sub-Poissonian photon statistics and squeezing. In addition, phase distribution function and quantum phase fluctuation have been studied. These properties are examined for various combinations of number of photon addition and/or subtraction and Fock parameter. The examination has revealed that photon addition generally improves nonclassicality, and this advantage enhances for the large (small) values of displacement parameter using photon subtraction (Fock parameter). The higher-order sub-Poissonian photon statistics is only observed for the odd orders. In general, higher-order nonclassicality criteria are found to detect nonclassicality even in the cases when corresponding lower-order criteria failed to do so. Photon subtraction is observed to induce squeezing, but only large number of photon addition can be used to probe squeezing for large values of displacement parameter. Further, photon subtraction is found to alter the phase properties more than photon addition, while Fock parameter has an opposite effect of the photon addition/subtraction. Finally, nonclassicality and non-Gaussianity is also established using Q function.

Immature platelet fraction related parameters in the differential diagnosis of thrombocytopenia

The pathogenesis of thrombocytopenia can be divided into increased destruction (ID) of platelets in the peripheral blood and decreased production (DP) of platelets in the bone marrow. This study aimed to analyze the efficacy of immature platelet fraction (IPF) related parameters, including the IPF count (IPF#), IPF percentage (IPF%) and highly fluorescence IPF percentage (H-IPF%), measured by XN-9000, in the differential diagnosis of thrombocytopenia. One hundred and twenty healthy volunteers were enrolled in the healthy control (HC) group, and 180 thrombocytopenia patients were grouped into either the increased destruction (ID) group or the decreased production (DP) group according to their final diagnosis. IPF# was significantly lower in the DP group than in the ID and HC groups (P < .01). Among the three groups, the ID group had the highest IPF% and H-IPF%, and the HC group had the lowest IPF% and H-IPF%. The differences between the three groups were all statistically significant (P < .01). In differentiating the ID patients from the DP patients, the areas under the operating characteristics curve of IPF#, IPF% and H-IPF% were 0.859, 0.944 and 0.930, respectively. False positive rates were below 0.04 when IPF#, IPF% and H-IPF% were above 2.65, 7.55 and 2.35, respectively. IPF related parameters showed high efficacy in the differential diagnosis of thrombocytopenia. However, due to the small numerical values of the IPF related parameters in some thrombocytopenia patients, the fluctuations of IPF% and H-IPF% should also be taken into consideration. Though H-IPF% is a new parameter, its effectiveness in the differential diagnosis of thrombocytopenia is not better than IPF%’s.

Physical and thermodynamic properties of quartic quasitopological black holes and rotating black branes with a nonlinear source

In this paper, we find the solutions of quartic quasitopological black holes and branes coupled to logarithmic and exponential forms of nonlinear electrodynamics. These solutions have an essential singularity at $r=0$. Depending on the value of charge parameter $q$, we have an extreme black hole/brane, a black hole/brane with two horizons or a naked singularity. For small values of parameter $q$, the solutions lead to a black hole/brane with two horizons. The values of the horizons are independent of the values of quasitopological parameters and depend only on the values of $q$, dimensions $n$, nonlinear parameter $\beta$ and mass parameter. Also, the solutions are not thermally stable for dS and flat spacetimes. However, AdS solutions are stable for $r_{+}>{r_{+}}_{\rm{ext}}$ which the temperature is zero for $r_{+}={r_{+}}_{\rm{ext}}$. The value of ${r_{+}}_{\rm{ext}}$ also depends on the values of parameters $q$, $\beta$, $n$ and $m$. As the value of ${r_{+}}_{\rm{ext}}$ decreases, the region of stability becomes larger. We also use HPEM metric to probe GTD formalism for our solutions. This metric is successful to predict the divergences of the scalar curvature exactly at the phase transition points. For large values of parameter $\Xi$, the black hole/brane has a transition to a stable state and stays stable.

Analysis of mathematical model of fractional viscous fluid through a vertical rectangular channel

Unsteady motion of a viscous fluid passing through a vertical channel with MHD (magnetohydrodynamics) effect has been analyzed in this manuscript. Fractional model is developed by two approaches, namely; Caputo fractional time derivatives with singular kernel and Caputo–Fabrizio fractional time derivatives with non-singular kernel. Analytical solutions have been obtained via Laplace transform method after converting the governing equations into dimensionless form and presented graphical analysis of the obtained results in terms of comparison. The effect of fractional and other flow parameters on temperature, concentration and velocity fields is seen, respectively. As a result, we have found that for the physical model with fractional derivative of Caputo–Fabrizio, temperature, concentration and velocity have greater values in comparison with Caputo one. It is also noted that velocity has shown dual nature for large and small time. Further, rates of heat and mass transfer and skin friction can also be enhanced for the small values of non-integer order parameter and are presented in Table 1.

Potential softening and eccentricity dynamics in razor-thin, nearly-Keplerian discs.

In many astrophysical problems involving discs (gaseous or particulate) orbiting a dominant central mass, gravitational potential of the disc plays an important dynamical role. Its impact on the motion of external objects, as well as on the dynamics of the disc itself, can usually be studied using secular approximation. This is often done using softened gravity to avoid singularities arising in calculation of the orbit-averaged potential — disturbing function — of a razor-thin disc using classical Laplace-Lagrange theory. We explore the performance of several softening formalisms proposed in the literature in reproducing the correct eccentricity dynamics in the disc potential. We identify softening models that, in the limit of zero softening, give results converging to the expected behavior exactly, approximately or not converging at all. We also develop a general framework for computing secular disturbing function given an arbitrary softening prescription for a rather general form of the interaction potential. Our results demonstrate that numerical treatments of the secular disc dynamics, representing the disc as a collection of N gravitationally interacting annuli, are rather demanding: for a given value of the (dimensionless) softening parameter, ς ≪ 1, accurate representation of eccentricity dynamics requires N ∼ Cς−χ ≫ 1, with C ∼ O(10), 1.5 ≲ χ ≳. In discs with sharp edges a very small value of the softening parameter ς (≲ 10−3) is required to correctly reproduce eccentricity dynamics near the disc boundaries; this finding is relevant for modelling planetary rings.

A plane-wave formulation and numerical analysis of elastic multicomponent inverse scattering series internal multiple prediction

Internal multiple prediction and removal is a critical component of seismic data processing prior to imaging, inversion, and quantitative interpretation. Inverse scattering series methods predict multiples without identification of generators, and without requiring a velocity model. Land environments present several challenges to the inverse scattering series prediction process. This is particularly true for algorithm versions that explicitly account for elastic conversions and incorporate multicomponent data. The theory for elastic reference medium inverse scattering series internal multiple prediction was introduced several decades ago, but no numerical analysis or practical discussion of how to prepare data for it currently exists. We have focused our efforts on addressing this gap. We extend the theory from 2D to 3D, analyze the properties of the input data required by the existing algorithm, and, motivated by earlier research results, reformulate the algorithm in the plane-wave domain. The success of the prediction process relies on the ordering of events in either pseudodepth or vertical traveltime being the same as the ordering of reflecting interfaces in true depth. In elastic-multicomponent cases, it is difficult to ensure that this holds true because the events to be combined may have undergone multiple conversions as they were created. Several variants of the elastic-multicomponent prediction algorithm are introduced and examined for their tendency to violate ordering requirements (and create artifacts). A plane-wave domain prediction, based on elastic data that have been prepared (1) using variable, “best-fit” velocities as reference velocities, and (2) with an analytically determined vertical traveltime stretching formula, is identified as being optimal in the sense of generating artifact-free predictions with relatively small values of the search parameter [Formula: see text], while remaining fully data driven. These analyses are confirmed with simulated data from a layered model; these are the first numerical examples of elastic-multicomponent inverse scattering series internal multiple prediction.

Revisiting singlino dark matter of the natural Z3-symmetric NMSSM in the light of LHC

Inspired by the fact that relatively small values of the effective higgsino mass parameter of the Z3-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM) could render the scenario ‘natural’, we explore the plausibility of having relatively light neutralinos and charginos (the electroweakinos or the ewinos) in such a scenario with a rather light singlino-like Lightest Supersymmetric Particle (LSP), which is a Dark Matter (DM) candidate, and singlet-dominated scalar excitations. By first confirming the indications in the existing literature that finding simultaneous compliance with results from the Large Hadron Collider (LHC) and those from various DM experiments with such light states is, in general, a difficult ask, we proceed to demonstrate, with the help of a few representative benchmark points, how exactly and to what extent could such a highly motivated ‘natural’ setup with a singlino-like DM candidate still remains plausible.

Conjectures about the ground-state energy of the Lieb-Liniger model at weak repulsion

We develop an alternative description to solve the problem of the ground-state energy of the Lieb-Liniger model that describes one-dimensional bosons with contact repulsion. For this integrable model we express the Lieb integral equation in the representation of Chebyshev polynomials. The latter form is convenient to efficiently obtain very precise numerical results in the singular limit of weak interaction. Such highly precise data enable us to use the integer relation algorithm to discover the analytical form of the coefficients in the expansion of the ground-state energy for small values of the interaction parameter. We obtained the first nine terms of the expansion using quite moderate numerical efforts. The detailed knowledge of behavior of the ground-state energy on the interaction immediately leads to exact perturbative results for the excitation spectrum.

A hybrid numerical study of bacteria gliding on a shear rate-dependent slime

Various phylogenetic categorized groups of rod-shaped bacteria exhibit the gliding mechanism over solid surfaces without any aid of flagella. It is postulated that such gliding bacteria push themselves by means of generating waves in their own surface and leave an adhesive trail of slime. In the subsequent analysis, two different non-Newtonian fluid models i.e., Bingham model and Carreau model are used to describe the complex rheology of the slime. We assumed that the solid substrate present beneath the bacterium is inclined at a certain angle to the horizontal. We derive equations governing the flow for each fluid model under long wavelength assumption. In order to calculate the bacterial gliding speed and slime flow rate we employ finite difference method combined with Broyden root finding algorithm. The obtained speed and energy dissipation are plotted for various inclination angles and rheological parameters. Moreover, by using the realistic (calculated) pairs of the glider’s speed and flow rate, the flow patterns are shown graphically and discussed in detail. The present work is an extension to our previous study Ali et al. (2016) in which a reduced constitutive equation of Carreau model was solved by perturbative approach to obtain the gliding speed on a straight substrate valid for small values of rheological parameters. The most significant outcome of the present numerical work is that the speed of gliding bacteria can be controlled by adjusting the slime rheology and inclination angle.

Limitation of the Lee–Huang–Yang interaction in forming a self-bound state in Bose–Einstein condensates

The perturbative Lee–Huang–Yang (LHY) interaction proportional to n3∕2, where n is the density, creates an infinitely repulsive potential at the center of a Bose–Einstein condensate (BEC) with net attraction, which stops the collapse to form a self-bound state in a dipolar BEC and in a binary BEC. However, recent microscopic calculations of the non-perturbative beyond-mean-field (BMF) interaction indicate that the LHY interaction is valid only for very small values of gas parameter x. We show that a realistic non-perturbative BMF interaction can stop collapse and form a self-bound state only in a weakly attractive binary BEC with small x values (x⪅0.01), whereas the perturbative LHY interaction stops collapse for all attractions. We demonstrate these aspects using an analytic BMF interaction with appropriate weak-coupling LHY and strong coupling limits.

Semi-analytical approaches for the nonlinear dynamics of a taut string subject to a moving load

The nonlinear behavior induced by a moving force on the dynamics of a nonlinear taut string is investigated. In these cases, classic perturbation solutions are only applicable to the weakly nonlinear problem and pertain to small values of dimensionless parameters governing the system. A change of coordinate that is dependent on the nonlinear quasi-static response of the string enables the formulation of a new set of governing equations for an incremental dynamic variable. These new equations are obtained using a closed-form expression for the nonlinear quasi-static displacement of the string. The solution to the linearized form of the governing equations allows us to compute the effective dynamic response even in the presence of strong nonlinearities, for which string dynamic tensions can reach values over twice the static ones. The proposed procedure also shows good reduction characteristics and permits a description of the dynamic response using a small number of eigenfunctions. Applications of the procedure show that, unless the speed of the moving load is sufficiently large, the nonlinear behavior of the string is captured by the quasi-static solution, whereas the dynamics are captured by the linearized equations of motion about this state.