Narrow Results

In this paper, we investigate the kinetic energy and angular momentum of free particles in a class of rotating cylindrical gravitational wave spacetimes, using the Noether symmetry approach. For that purpose, we determine the conserved quantities and subsequently analyze them for the velocities of free particles in the spacetimes, thereby simplifying the relationship between velocities and coordinates. Our analysis demonstrates that arbitrary choices of metric coefficients lead to fluctuations in the velocity of free particles, thereby causing variations in their kinetic energy under the influence of rotating cylindrical gravitational waves. Furthermore, we derive expressions for the angular momentum imparted to free particles by these waves, considering various scenarios for metric coefficients. Interestingly, we observe that the angular momentum of free particles initially experiences an increase over time but eventually starts to decrease after a certain duration.

A computational analysis has been performed to study the flow instability of two-parallel wall motions in a Cuboidal enclosure incorporated by a cylinder under different radii sizes. A numerical methodology based on the Finite Volume Method (FVM) and a full Multigrid acceleration is utilized in this paper. Left and right parallel walls of the cavity are maintained driven and all the other walls completing the domain are motionless. Different radii sizes ($R=0.075$, 0.1, 0.125, 0.15 and 0.175) are employed encompassing descriptive Reynolds numbers that range three orders of magnitude 100, 400 and 800 for the steady state. The obtained results show positions $R=0.15$ and $R=0.175$ of the inner cylinder promote cell distortion. Also, when the radius equates to $R=0.15$, it may lead to the birth of tertiary cells at $\mathrm{\text{Re}}=400$ which are more developed for $\mathrm{\text{Re}}=800$. Thereafter, analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a Hopf bifurcation. A nonuniform variation with the radius size of the inner cylinder is observed. Otherwise said, elongating the radius of the cylinder leads to decrease in the critical Reynolds number. Hence, the acceleration of the unsteadiness is realized. On the other hand, by further increasing Reynolds number more than the critical value from 1200 to 2100, we note that the kinetic energy is monotonously increasing with Reynolds number and a stronger motion in the velocity near the rear wall of the enclosure is observed. Furthermore, the symmetry of flow patterns observed in the steady state has been lost. Therefore, a systematic description of various effects illuminating the optimum geometrical parameters to achieve effective flow behavior in those systems has been successfully established through this paper.

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

At the even-denominator filling factor ν=P/Q, even Q, a fermionic Quantum Hall (QH) state is shown to be developed at the lowest temperatures. In this state, formed by the composite (c-) fermions, each with an electron and the even number Q of flux quanta (fluxons), the conductivity σ≡J/E(J=current density, E=applied field) becomes a universal constant (e²/h)Q^-2 as the temperature T approaches zero while the Hall conductivity σ_H≡J/E_H(E_H=Hall field) becomes approximately equal to (e²/h)(P/Q).

In this work, three models of the nonlinear Schrödinger equation are looked at to see if traveling wave solutions have unique structures. “The generalized Korteweg–de Vries, (2+1)-dimensional Ablowitz–Kaup–Newell–Segur, and the Maccari models” are among the examined systems. The kinetic energy operator is affected by where the mass is, how it changes over time, and how the kinetic energy operator is shown. Using the generalized Riccati expansion method, new soliton wave solutions are constructed for the models that have been looked at. Several different graphics depict the numerical simulations of the deduced answers. Verifying and improving these methods (Mathematica 13.1) means checking to see if they are right and re-entering the results into the models.

In the present study, a three-dimensional discontinuous deformation analysis (3D DDA) method was developed and used to investigate the effect of slope geometrical characteristics on rockfall behaviors. The slope geometrical characteristics of rockfall, such as the slope height, slope angle and slope shape, were summarized, and the corresponding calculation models were proposed. The algebraic computation and contact mechanics of the three-dimensional (3D) global contact theory were illustrated and implemented into the 3D DDA method. The accuracy of the developed 3D DDA method was verified through the four basic movement forms of rockfall: freefalling (oblique projectile), sliding, rolling and bouncing. Numerical examples were performed to study rockfall behaviors under different slope geometrical characteristics by analyzing the kinetic energy or velocity conversion, motion trajectories, and damage degree and range of moving blocks. The results demonstrate that the 3D DDA method can accurately simulate rockfall movement, which is significantly affected by slope geometrical characteristics. Furthermore, some suggestions for slope excavation and protection were put forward.

On rockfall slopes, trees can play a natural and efficient protective role in preventing the occurrence of rockfall disasters. This paper presents a study on the tree barrier effect on rockfall based on a three-dimensional discontinuous deformation analysis (3D DDA) method. The tree barrier effect on rockfall is studied considering the 3D spatial effect of rockfall movement and the 3D spatial distribution of trees. The basic movement forms and collision modes of rockfall related to the tree barrier are classified, and the impact factors of tree arrangements on rockfall are proposed. The contact mechanism employed in the 3D DDA method is illustrated, and the accuracy of the 3D DDA rockfall simulation is verified by comparing with the results obtained from laboratory experiments. Numerical examples are conducted to study the effect of the tree barrier on rockfall, and general laws are derived by analyzing the variation of kinetic energies and motion trajectories of moving blocks. The results show that the 3D DDA method can effectively predict the 3D motion behaviors of rockfall and assess the tree barrier effect. Furthermore, a reasonable arrangement of trees or a combination of protective facilities and trees can prevent or mitigate the rockfall hazards.

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

There are two types of warped product pseudo-slant submanifolds, $M_{𝜃}{\times }_f{M}_{\perp }$ and $M_{\perp }{\times }_f{M}_{𝜃}$, in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold $M_{\perp }{\times }_f{M}_{𝜃}$ in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber $M_{𝜃}$ is a slant submanifold. Moreover, the equality is verified for depending on what $M_{𝜃}$ and $M_{\perp }$ are, and also we show that if the equality holds, then $M_{\perp }{\times }_f{M}_{𝜃}$ is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if $M_{\perp }{\times }_f{M}_{𝜃}$ is a totally real warped product submanifold.

The upper bound of Ricci curvature conjecture, also known as Chen-Ricci conjecture, was formulated by Chen [B. Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J.41 (1999) 33–41] and modified by Tripathi [M. M. Tripathi, Improved Chen–Ricci inequality for curvature-like tensors and its applications, Diff. Geom. Appl.29 (2011) 685–698]. In this paper, first, we define partially minimal isometric immersion of warped product manifolds. Then, we derive a fundamental theorem for Ricci curvature via partially minimal isometric immersions from a warped product pointwise bi-slant submanifolds into complex space forms. Some applications are constructed in terms of Dirichlet energy function, Hamiltonian, Lagrangian and Hessian tensor due to appearance of the positive differential function in the inequality.

The flow of a superfluid film adsorbed on a porous medium can be modeled by a meromorphic differential on a Riemann surface of high genus. In this paper, we define the mixed Hodge metric of meromorphic differentials on a Riemann surface and justify using this metric to approximate the kinetic energy of a superfluid film flowing on a porous surface.

In order to solve to the technical bottleneck that powder is easy to reunite and without refining in the vibration ultrafine grinding (UFG) technology, the energy field of medium flow was studied by analyzing crushing energy and energy transfer. The numerical simulation model of medium flow based on Particle Flow Code (PFC) was established. By setting four kinds of working conditions of amplitude and frequency, the dynamic graphics and curves of the energy field (such as kinetic energy, strain energy, velocity field, force chain and so on) were obtained. In the situation of mid-frequency with large amplitude, the average speed of front medium flow was 1.3–5.03 times that of others and the low-energy region was decreased by 6% to 10%. The largest kinetic energy and strain energy were 3.25 and 2.94 times the average value of others, respectively. The diamond UFG was analyzed in new vibration mills under the conditions of low frequency with large amplitude and mid-frequency with large amplitude. Utilizing a laser particle size analyzer, it was discovered that the particle sizes d(50) in these two models were 3.840$\mu$m and 0.260$\mu$m and bandwidths were 9.940$\mu$m and 3.825$\mu$m. This highlights the effect of mid-frequency with large amplitude in particle refining and bandwidth narrowing, which is of great importance in the fields of ultra-hard particle refining research and energy utilization.