The properties of nonplanar (cylindrical and spherical) quantum dust ion-acoustic (QDIA) solitary waves in an unmagnetized quantum dusty plasma, whose constituents are inertial ions, Fermi electrons with quantum effect, and negatively charged immobile dust particles, are investigated by deriving the modified Gardner (MG) equation. The reductive perturbation method is employed to derive the MG equation, and the basic features of nonplanar QDIA Gardner solitons (GSs) are analyzed. It has been found that the basic characteristics of GSs, which are shown to exist for the value of Zdnd0/ni0 around 2/3 (where Zd is the number of electrons residing on the dust grain surface, and nd0 and ni0 are, respectively, dust and ion number density at equilibrium), are different from those of the Korteweg-de Vries solitons, which do not exist for the value of Zdnd0/ni0 around 2/3. It is also seen that the properties of nonplanar QDIA GSs are significantly different from those of planar ones.
In this paper, the implementations of two reinforcement learnings namely, Q learning and deep Q network (DQN) on the Gazebo model of a self balancing robot have been discussed. The goal of the experiments is to make the robot model learn the best actions for staying balanced in an environment. The more time it can remain within a specified limit, the more reward it accumulates and hence more balanced it is. We did various tests with many hyperparameters and demonstrated the performance curves.Electronic supplementary materialThe online version of this article (10.1186/s40638-018-0091-9) contains supplementary material, which is available to authorized users.
3-D topographic surfaces (“topos”)
can be generated
to visualize how pH behaves during titration and dilution procedures.
The surfaces are constructed by plotting computed pH values above
a composition grid with volume of base added in one direction and
overall system dilution on the other. What emerge are surface features
that correspond to behavior in aqueous solutions. Equivalence point
breaks become cliffs that pinch out with dilution. Buffer effects
become plateaus. Dilution alone generates 45° ramps. Limitations
of the Henderson–Hasselbalch equation can be seen by noting
the conditions over which a plateau remains relatively flat. Because
dissociation is driven by dilution, the surfaces demonstrate when
the solution of a weak acid becomes indistinguishable from that of
a strong acid. Surfaces are presented for hydrochloric acid, HCl (a
strong acid); acetic acid, CH3COOH (a weak monoprotic acid);
oxalic acid, HOOCCOOH (a weak diprotic acid) and l-histidine
dihydrochloride, C6H9N3O2·2HCl (a weak triprotic acid). Supplementary materials include
suggested use of topos in lecture, as worksheets and in support of
laboratory activities for first-year college courses and third-year
analytical chemistry courses. Also provided is pH TOPOS, the macro-enabled
spreadsheets that quickly generate surfaces for any mono-, di-, or
triprotic acid desired. Only a change of acid dissociation constants, K
a values, is required.
Nonplanar (cylindrical and spherical) double layers (DLs) in a quantum dusty plasma (composed of inertial ions, Fermi electrons and negatively charged immobile dust particles) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the quantum dust ion-acoustic (QDIA) waves is derived, and its nonplanar DL solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with both positive and negative potentials, are obtained. It has been found that the existence of small but finite-amplitude electrostatic DLs depends on μ = Zdnd0/ni0 (where Zd is the number of electrons residing onto the dust grain surface, and nd0 and ni0 are, respectively, the dust and ion number density at equilibrium) as well as the quantum diffraction parameter H. It has also been found that the propagation characteristics of nonplanar QDIA DLs are significantly different from those of the planar ones.
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