Starting from the hydrodynamic equations of binary granular mixtures, we derive an evolution equation for the relative velocity of the intruders, which is shown to be coupled to the inertia of the smaller particles. The onset of Brazil-nut segregation is explained as a competition between the buoyancy and geometric forces: the Archimedean buoyancy force, a buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. We show that inelastic dissipation strongly affects the phase diagram of the Brazil nut phenomenon and our model is able to explain the experimental results of Breu et al. [16].

We present a hydrodynamic theoretical model for "Brazil nut" size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local "granular temperature". The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.

We study chaotic functions that are exact solutions to nonlinear maps. A generalization of these functions cannot be expressed as a map of type X n+1 = g(X n , X n−1 , . . . , X n−r+1 ).The generalized functions can produce truly random sequences. Even if the initial conditions are known exactly, the next values are in principle unpredictable from the previous values. Although the generating law for these random sequences exists, this law cannot be learned from observations.

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We investigate generalized soliton-bearing systems in the presence of external perturbations. We show the possibility of the transport of solitons using external waves, provided the waveform and its velocity satisfy certain conditions. We also investigate the stabilization and transport of bubbles using external perturbations in 3D-systems. We also present the results of real experiments with laser-induced vapor bubbles in liquids.

PACS. 05.45.-a -Nonlinear dynamics and nonlinear dynamical systems. PACS. 42.65.Sf -Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics. PACS. 05.45.Vx -Communication using chaos.Abstract. -We show that functions of type Xn = P [Z n ], where P [t] is a periodic function and Z is a generic real number, can produce sequences such that any string of values Xs, Xs+1, ..., Xs+m is deterministically independent of past and future values. There are no correlations between any values of the sequence. We show that this kind of dynamics can be generated using a recently constructed optical device composed of several Mach-Zehnder interferometers. Quasiperiodic signals can be transformed into random dynamics using nonlinear circuits. We present the results of real experiments with nonlinear circuits that simulate exponential and sine functions. Other papers have shown that even chaotic communication systems can be cracked if the chaos is predictable [7,8].In the present Letter we will show that using the same experimental setup of Ref.[6] with some small modifications and also other physical systems, it is possible to construct random maps that generate completely unpredictable dynamics.S. Ulam and J. von Neumann [9,10] proved that the logistic map X n+1 = 4X n (1 − X n ) can be solved using the explicit function X n = sin 2 [θπ2 n ]. Other chaotic maps are solvable exactly using, e.g., the functions X n = sin 2 [θπk n ], X n = cos[θπk n ], and other functions of type X n = P [k n ], where k is an integer [11][12][13][14]. For instance, X n = sin 2 [θπ3 n ] is the exact

Based on the Boltzmann-Enskog kinetic theory, we develop a hydrodynamic theory for the well known (reverse) Brazil nut segregation in a vibro-fluidized granular mixture. Under strong shaking conditions, the granular mixture behaves in some ways like a fluid and the kinetic theory constitutive models are appropriate to close the continuum balance equations for mass, momentum and granular energy. Using this analogy with standard fluid mechanics, we have recently suggested a novel mechanism of segregation in granular mixtures based on a competition between buoyancy and geometric forces: the Archimedean buoyancy force, a pseudo-thermal buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. For a mixture of perfectly hard-particles with elastic collisions, the pseudo-thermal buoyancy force is zero but the intruder has to overcome the net compressive geometric force to rise. For this case, the geometric force competes with the standard Archimedean buoyancy force to yield a threshold density-ratio, R ρ1 = ρ l /ρ s < 1, above which the lighter intruder sinks, thereby signalling the onset of the reverse buoyancy effect. For a mixture of dissipative particles, on the other hand, the non-zero pseudo-thermal buoyancy force gives rise to another threshold density-ratio, R ρ2 ( > R ρ1 ), above which the intruder rises again. Focussing on the tracer limit of intruders in a dense binary mixture, we study the dynamics of an intruder in a vibrofluidized system, with the effect of the base-plate excitation * being taken into account through a 'mean-field' assumption. We find that the risetime of the intruder could vary non-monotonically with the density-ratio. For a given size-ratio, there is a threshold density-ratio for the intruder at which it takes the maximum time to rise, and above(/below) which it rises faster, implying that the heavier (and larger) the intruder, the faster it ascends. The peak on the risetime curve decreases in height and shifts to a lower density-ratio as we increase the pseudo-thermal buoyancy force. The rise (/sink) time diverges near the threshold density-ratio for reverse-segregation. Our theory offers a unified description for the (reverse) Brazil-nut segregation and the non-monotonic ascension dynamics of Brazil-nuts.

The intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media. We propose a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder. From the analytic solution of the segregation velocity we can analyze the transition from the upward to downward intruder's movement.