21,783 research outputs found
Discrete embedded solitons
No full textWe address the existence and properties of discrete embedded solitons (ESs), that is localised waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both Chi(2) (second-harmonic generation) and Chi(3) (Kerr) nonlinearities, for which a rich family of ESs are known to occur in the continuum limit. First, a simple motivating problem is considered, in which the Chi(3) nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From the properties of such maps, it is shown that (unlike ordinary gap solitary waves), discrete ESs have the same codimension as their continuum counterparts. A speci c numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a speci c reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case
A global investigation of solitary-wave solutions to a two-parameter model for water waves
No full textThe model equation (2r''''/15)-(br'')+(ar)+(3r^2/2)-((r')^2/2)+[rr']'=0 arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravitycapillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation. At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of solitary waves of elevation as local bifurcation phenomena in a particular parameter regime; the second, larger, issue is the determination of the global bifurcation picture for solitary waves. Given that the above equation is a good model for solitary waves of depression, it seems natural to study the above issues for this equation; they are comprehensively treated in this article. The equation is found to have branches of solitary waves of elevation bifurcating from the trivial solution in the appropriate parameter regime, one of which is described by an explicit solution. Numerical and analytical investigations reveal a rich global bifurcation picture including multi-modal solitary waves of elevation and depression together with interactions between the two types of wave. There are also new orbit-flip bifurcations and associated multi-crested solitary waves with non-oscillatory tail
Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities
No full textThis paper continues an investigation into a one-dimensional lattice equation that models the light field in a system comprised of a periodic array of pumped optical cavities with saturable nonlinearity. The additional effects of a spatial gradient of the phase of the pump field are studied, which in the presence of loss terms is shown to break the spatial reversibility of the steady problem. Unlike for continuum systems, small symmetry-breaking is argued to not lead directly to moving solitons, but there remains a pinning region in which there are infinitely many distinct stable stationary solitons of arbitrarily large width. These solitons are no-longer arranged in a homoclinic snaking bifurcation diagrams, but instead break up into discrete isolas. For large enough symmetry-breaking, the fold bifurcations of the lowest intensity solitons no longer overlap, which is argued to be the trigger point of moving localised structures. Due to the dissipative nature of the problem, any radiation shed by these structures is damped and so they appear to be true attractors. Careful direct numerical simulations reveal that branches of the moving solitons undergo unsual hysteresis with respect to the pump, for sufficiently large symmetry breaking
Friction-induced reverse chatter in rigid-body mechanisms with impacts
No full textThe focus of this paper is on the possibility of formulating a consistent and unambiguous forward-simulation model of planar rigid-body mechanical systems with isolated points of intermittent or sustained contact with rigid constraining surfaces in the presence of dry friction. In particular, the analysis considers paradoxical ambiguities associated with the coexistence of sustained contact and one or several alternative forward trajectories that include phases of free-flight motion. Special attention is paid to the so-called Painlev´e paradoxes where sustained contact is possible even if the contact-independent contribution to the normal acceleration would cause contact to cease. Here, through taking the infinite-sti ness limit of a compliant contact model, the ambiguity in the case of a condition of sustained stick is resolved in favour of sustained contact, whereas the ambiguity in the case of a condition of sustained slip is resolved by eliminating the possibility of reaching such a condition from an open set of initial conditions. A more significant challenge to the goal of an unambiguous forward-simulation model is a orded by the discovery of open sets of initial conditions and parameter values associated with the possibility of a left accumulation point of impacts or reverse chatter a transition to free flight through an infinite sequence of impacts with impact times accumulating from the right on a limit point and with impact velocities diverging exponentially away from the limit point, even where the contact-independent normal acceleration supports sustained contact. In this case, the infinite-sti ness limit of the compliant formulation establishes that, under a specific set of open conditions, the possibility of reverse chatter in the rigid-contact model is an irresolvable ambiguity in the forward dynamics based at the terminal point of a phase of sustained slip. Indeed, as the existence of a left-accumulation point of impacts is associated with a one-parameter family of possible forward trajectories, the ambiguity is of infinite multiplicity. The conclusions of the theoretical analysis are illustrated and validated through numerical analysis of an example single-rigid-body mechanical model
The stability of automatic ball balancers
No full textOne realisation of an automatic balancer uses two or more balls that are free to travel in a race, filled with a viscous fluid, at a fixed distance from the shaft centre. The objective is for the balls to position themselves so that they counteract any residual unbalance. The fact that no external force is required to achieve balance, that is the system is passively controlled, means that the balancer is potentially able to cope with a time-varying unbalance. Typical applications include optical disc drives and machine tools. However, the usefulness of this device depends on the balanced steady state solution being achievable and stable. This paper describes a dynamic model of a Jeffcott rotor with an automatic balancer and provides a non-linear analysis of its dynamics to determine steady states and their bifurcations as parameters are varied. The pseudospectra of the linearization of the system about a balanced steady state solution are computed. This approach allows the eigenvalues that are most sensitive to perturbation to be quantified. Furthermore, how the sensitivity of the eigenvalues influences the transient response may be determined. These tools will help to design reliable and robust automatic balancers
Homoclinic orbits in reversible systems II : multi-bumps and saddle-centres
No full textThis article extends a review by the author in Physica D, vol.112, pp.158-186 of the theory and application of homoclinic orbits to equilibria in even-order, time-reversible systems of autonomous ordinary differential equations, either Hamiltonian or not. Recent results in two directions are surveyed. First, a heteroclinic connection between a saddle-focus equilibrium and a periodic orbit is shown to arise from a certain codimension-two local bifurcation; a degenerate Hamiltonian-Hopf bifurcation. Under a transversality hypothesis, perturbation from normal form causes this isolated solution to break into a snaking bifurcation curve under which a primary homoclinic becomes a multi-bump with arbitrarily many bumps. Taking as a model a fourth-order equation arising in many contexts, the snaking is terminated by the existence of a heteroclinic connection to an equilibrium. Second, multi-bump homoclinic orbits are considered in the case where the equilibrium is a four-dimensional saddle-centre (having two real and two imaginary eigenvalues). If the system is Hamiltonian, then it is known that a sign condition determines whether or not cascades of multi-bumps accumulate on the parameter values of a primary homoclinic solution. For non-Hamiltonian reversible systems cascades always occur, albeit from one sign of parameter perturbation only. Finally, aided by numerical methods, possible applications are considered to localised cylindrical shell buckling and to a generalised massive Thirring model arising in nonlinear optics
Ittijahat Abi Dhu'ayb Al-Hudhali fi Qasidatihi Ar-Ritsa’
No full textThis article aims to know Ittijahat of Abu Dhu’ayb Al-Hudhali in his poem of Ritsa’. Ittijahat in this study is a description of the poet's tendency to divide Ar-Ritsa', namely Nadb and Ta'ziyah. Ar-Ritsa 'is one of the various forms of Arabic poetry. To analyze the discussion problem, the author uses descriptive analysis method, because this method is very appropriate to find out the picture and state of a thing by describing it in as much detail as possible based on the facts found in the data in question. The results obtained are: In the beginning of the poem, he tends to mourn (Nadb) their five children. He describes in it that he does not stop crying and has trouble sleeping until he becomes weak emaciated due to the intensity of the grief, pain and worries that dominated in his pysche. As for the middle of the poem to the end, the poet turns to the consolation (Ta’ziyah) of his children’s death, as he reflects on the reality of life and death, the poet declares that death is inevitable for every human being that he must accept it and let it go, which the poet portrayed in the exciting narrative style. The story is divided into three stories: the zebra, the bull of the beast, and the two knights.</jats:p
Bifurcation analysis of surge and rotating stall in the Moore-Greitzer compression system
No full textA simple compression system model, described by a set of three ordinary nonlinear differential equations (the Moore-Greitzer model) is studied using bifurcation analysis to give a qualitative understanding of the presence of surge and rotating stall. Firstly, three parameter values are chosen and a reduced planar system is studied to detect the local bifurcations of pure surge modes. The global bifurcation diagrams are then completed with the help of the continuation software AUTO. A special feature of this 2D system is a set of parameter values where two Takens-Bogdanov points merge. As a next step, the interaction of surge and rotating stall modes is analysed using the same branch tracking technique. Several novel bifurcation scenarios are described. Two-parameter bifurcation maps are computed and a satisfactory agreement with experimental results is found. An explanation is given for the onset of deep surge, rotating stall, classic surge and the hysteresis effects experienced in measurements
Program “I’dad Lughowi” dalam Upaya Membekali Kemampuan Bahasa Arab Mahasiswa STIBA Ar-Raayah, Sukabumi
No full textNowdays, Arabic already has its own charm. Apart from the Al-Quran and Hadith as sources of Islamic Shari'a which are imported from the original source in Arabic, the emergence of scientific disciplines linked to Shari'a adds to the public's attraction and interest in studying Shari'a directly from its Arabic sources. Arabic language learning is starting to emerge with various strategies and methods applied. Some are successful and others need review. In this article, the author wants to examine Arabic language learning in the STIBA Ar-Raayah i'dad lughowi program which is considered successful because it has produced many regional, national and even international achievements. This article aims to examine the background of students in the STIBA Ar-Raayah i'dad lughowi program, the teaching and learning activities of the i'dad lughowi program at STIBA Ar-Raayah and the examination system implemented in the i'dad lughowi program. This article is a case study at STIBA Ar-Raayah using a descriptive qualitative approach. The results found in this research are (1) the background of students in the STIBA Ar-Raayah i'dad lughowi program who come from various regions and schools, (2) learning using the Arabiyyah book Baina Yadaik by maximizing the direct method and activities outside the classroom, (4) a unique exam system with Al-Qur'an exams, subject exams, syahri exams, nihai exams, as well as a rosib system for students who do not reach the minimum completion criteria. The results and conclusions of this research can be used as a reference for Arabic language educational institutions to make them more effective in the future
Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation
No full textNumerical evidence is presented for the existence of stable heteroclinic cycles in large parameter regions of the one-dimensional complex Ginzburg–Landau equation (CGL) on the unit, spatially periodic domain. These cycles connect different spatially and temporally inhomogeneous time-periodic solutions as t?±?. A careful analysis of the connections is made using a projection onto five complex Fourier modes. It is shown first that the time-periodic solutions can be treated as (relative) equilibria after consideration of the symmetries of the CGL. Second, the cycles are shown to be robust since the individual heteroclinic connections exist in invariant subspaces. Thirdly, after constructing appropriate Poincaré maps around the cycle, a criteria for temporal stability is established, which is shown numerically to hold in specific parameter regions where the cycles are found to be of Shil’nikov type. This criterion is also applied to a much higher-mode Fourier truncation where similar results are found. In regions where instability of the cycles occurs, either Shil’nikov–Hopf or blow-out bifurcations are observed, with numerical evidence of competing attractors. Implications for observed spatio-temporal intermittency in situations modelled by the CGL are discusse
- …
