Context.
The Λ cold dark matter (ΛCDM) scenario is able to describe the Universe at large scales, but clearly shows some serious difficulties at small scales. The core-cusp question is one of these ...difficulties: the inner dark matter (DM) density profiles of spiral galaxies generally appear to be cored, without the
r
−1
profile that is predicted by
N
-body simulations in the above scenario.
Aims.
It is well known that in a more physical context, the baryons in the galaxy might backreact and erase the original cusp through supernova explosions. Before the efficiency and the presence of this effect is investigated, it is important to determine how wide and frequent the discrepancy between observed and
N
-body-predicted profiles is and what its features are.
Methods.
We used more than 3200 quite extended rotation curves (RCs) of good quality and high resolution of disk systems that included normal and dwarf spirals as well as low surface brightness galaxies. The curves cover all magnitude ranges. All these RCs were condensed into 26 coadded RCs, each of them built with individual RCs of galaxies of similar luminosity and morphology. We performed mass models of these 26 RCs using the Navarro-Frenk-White (NFW) profile for the contribution of the DM halo to the circular velocity and the exponential Freeman disk for the contribution of the stellar disk.
Results.
The fits are generally poor in all the 26 cases: in several cases, we find
χ
red
2
> 2. Moreover, the best-fitting values of three parameters of the model (
c
,
M
D
, and
M
vir
) combined with those of their 1
σ
uncertainty clearly contradict well-known expectations of the ΛCDM scenario. We also tested the scaling relations that exist in spirals with the outcome of the current mass modeling: the modeling does not account for these scaling relations.
Conclusions.
The results of testing the NFW profile in disk systems indicate that this DM halo density law cannot account for the kinematics of the whole family of disk galaxies. It is therefore mandatory for the success of the ΛCDM scenario in any disk galaxy of any luminosity or maximum rotational velocity to transform initial cusps into the observed cores.
We propose a modified structured secant relation to get a more accurate approximation of the second curvature of the least squares objective function. Then, using this relation and an approach ...introduced by Andrei, we propose three scaled nonlinear conjugate gradient methods for nonlinear least squares problems. An attractive feature of one of the proposed methods is satisfication of the sufficient descent condition regardless of the line search and the objective function convexity. We establish that the three proposed algorithms are globally convergent, under the assumption of the Jacobian matrix having full column rank on the level set for one, and without such assumption for the other two. Numerical experiments are made on the collection of test problems, both zero-residual and nonzero-residual, using the Dolan–Moré performance profiles. They show that the outperformance of our proposed algorithms is more pronounced on nonzero-residual as well as large problems.
In this paper, an adaptive chaos control is proposed for a typical vibratory piezomagnetoelastic energy harvesting system to return the chaotic behavior to a periodic one. Piezomagnetoelastic energy ...harvesting systems show chaotic behaviors in spite of harmonic input. Although, the chaotic behavior of the system gives higher output voltage than the periodic motion, it is preferred to the output voltage as this is periodic for charging a battery or a capacitor efficiently. Therefore, the chaos control is important in this system. The physical model is composed of the upper and lower piezoelectric layers on a cantilever taper beam, one attached tip magnet, and two external magnets (EM). Position of the EM is controlled by inputs. Firstly, chaotic and periodic regions are detected by utilizing the bifurcation diagrams, phase plan portrait, and Poincaré maps. Then an adaptive controller is proposed for controlling of the chaotic behaviors in the presence of uncertainty due to magnetic forces. The control law is derived based on the inverse dynamic method and the uncertainty elements of the controller are estimated using radial basis function (RBF) network. The weights of the RBF network are obtained using an adaptation law. The adaptation laws are derived based on Lyapunov stability theory and a projection operator. The distance of the tip magnet and the EM as well as the gap distance of two EM are used to control the chaotic behavior. Simulation results show that the proposed controller can return the chaotic motion to a periodic one in spite of the uncertainties in the magnetic forces.
Long-term underground cold-water cisterns had been used in old days in the hot and arid regions of Iran. These cisterns provide cold drinking water during warm seasons for local communities. In this ...paper, the thermal performance of an underground cold-water cistern during the withdrawal cycles in warm seasons is modeled. The cistern is located in the central region of Iran in the city of Yazd. Two approaches are used to model the heat transfer in the mentioned cistern. The first approach is meshless local Petrov–Galerkin (MLPG) method with unity test function and the second approach is artificial neural networks (ANN). For the ANN method, the multi layers perceptron (MLP) feed-forward neural network training by back propagation algorithm is used. Both methods are compared and a good agreement is observed between the MLPG and ANN results. The results show a stable thermal stratification in the cistern throughout the withdrawal cycle. The thermal stratification is linear in lower areas and exponential in upper areas. The exponential trend in the upper area is because of several factors such as: thermal exchange among the upper layers of water and the domed roof, transfer of mass and evaporation due to entry air from the wind towers.
Gait pattern affects the quality of a walking robot. In this paper, an optimum human-like gait generation method is proposed for a seven-link biped robot. This method utilizes kinematic constraints ...based on human-like motion. At first, the constraints are parameterized with unknown parameters. Then, an optimization problem is defined with an objective function and the kinematic constraints. The objective function includes the energy consumption and walking stability. Unknown parameters appearing in the constraints are determined by solving the optimization problem. Joint variables are obtained by integrating a velocity form of the kinematic constraints. This approach is carried out for gait planning of the seven-link biped robot and its results are presented. This method allows studying some effective parameters on the gait such as constant knee angle duration, and torso inclination is optimized for different speeds. Our studies indicate that as walking speed increases the knee should extend and the torso should lean forward further in order to maintain better stability. Moreover, energy consumption increases as the torso leans forward.
To improve upon numerical stability of the spectral conjugate gradient methods, two adaptive scaling parameters are introduced. One parameter is obtained by minimizing an upper bound of the condition ...number of the matrix involved in producing the search direction and the other one is obtained by minimizing the Frobenius condition number of the matrix. The proposed methods are shown to be globally convergent, under appropriate conditions. A comparative testing of the proposed methods and some efficient spectral conjugate gradient methods shows the computational efficiency of the proposed methods.
In order to get a higher order accuracy of approximating the Hessian matrix of the objective function, we use the chain rule and propose two modified secant equations. An interesting property of the ...proposed methods is that these utilize information from two most recent steps where the usual secant equation uses only the latest step information. The other point of interest to one of the proposed methods is that it makes use of both gradient and function value information. We show that the modified BFGS methods based on the new secant equations are globally convergent. The presented experimental results illustrate that the proposed methods are efficient.
Two new designs of wind towers were tested side by side with a conventional wind tower in the city of Yazd, Iran. All the towers were of identical dimensions. The two new designs were one with wetted ...column, consisting of wetted curtains hung in the tower column, and the other one with wetted surfaces, consisting of wetted evaporative cooling pads mounted at its entrance. The air temperature leaving the wind towers with evaporative cooling provisions were much lower than the air temperature leaving the conventional design, and its relative humidity much higher. The air-flow rate was reduced slightly in these new towers. It was found that the wind tower with wetted column performs better with high wind speeds whereas the tower with wetted surfaces performs better with low wind speeds. It is recommended that these new designs of wind towers should be manufactured in different sizes and incorporated in the designs of new buildings. They can replace the evaporative coolers currently employed in Iran, and other hot arid regions, with considerable saving in electrical energy consumption.
Magnetorheological dampers are used for semi-active control of the vehicles vibration because of their useful features such as reducing the dynamic tire forces, improvement the ride quality of the ...passengers and protection of the vehicle from rollover. The dynamic model of these dampers is nonlinear. Therefore, their nonlinear characteristics can lead to make the chaotic behaviour of the vehicle system if a suitable controller is not used. This paper focuses on the active control of the chaotic behaviour generated by the nonlinear model characteristics of the MR dampers in a typical heavy articulated vehicle. The vehicle nonlinear dynamic study is conducted by detecting the irregular regions using the bifurcation diagrams and Poincaré maps. Then, the active controller is proposed to control the chaotic behaviours. The control law was derived based on the backstepping method, and the stability analysis is performed by Lyapunov theorem. Then, optimal backstepping control is designed for controlling the chaos in the vehicle. The simulation results show the vehicle displacements can track a periodic desired motion. The robustness of the proposed controller is studied by inserting external disturbance force. The simulation results show that the vehicle body displacements converge to periodic desired path in spite of the existing external disturbance.
In this Letter, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive ...the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, r+, with the apparent horizon radius, r˜A, we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which shows the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology.
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