On the Dynamics of a Biomimetic Model of a Sympodial Tree: From Bifurcations Diagrams and 6D Basins of Attraction to Dynamical Integrity and Robustness

This work is concerned with a mechanical model of a sympodial tree with first-level branches, which has been shown to exhibit certain properties potentially suitable for biomimetic applications. To investigate these potential benefits further from the viewpoint of the system nonlinear behaviour under external periodic excitation, modern numerical tools related to the concept of dynamical integrity are either adjusted or newly developed for this system for the first time. First, multistable regions of interest are isolated from bifurcation diagrams and the effect of damping is investigated. Then, in order to obtain the corresponding basins of attraction of this highly dimensional model, an original computational procedure is developed that includes cell mapping with 406 cells, where each cell represents an initial condition required to construct the map. Full 6D basins are computed, and they are reported for various values of the damping parameter and the excitation frequency. Those basins are then used to calculate the dynamic integrity factors so that the dominant steady state can be determined. Finally, the integrity profiles are reported to illustrate how the robustness varies by changing the system parameters.

Semantics and poetics of the motif of voice in Gaito Gazdanov’s 1920-30 small prose: “Transformation” and “The disappearance of Ricardy”

The article is dedicated to research of the motif of voice in the semantic structure of Gaito Gazdanov’s 1920–30 small prose. Stories, representing the author's intentional object in his early works, were considered. The use of the methods of motif and intermedial analysis has made it possible to establish that dynamics of the stories’ “Transformation” and “The disappearance of Ricardy” plot is connected with the paradigm of metaphysic existence. The main components of this paradigm are translated into auditory imageries in Gazdanov’s narrative. A study of the texts has shown that during multiple variations audial imageries become motifs that mark existential-ontological problematics of works and form multifaceted art space. The motif of voice is highlighted as one of the main carriers of meaning in the motif system of both stories, which explicate the processes of consciousness of narrating subject and endowed with function of other character attributes. The motif of voice is also a dominant element of the intermedial code. Author’s intermedial strategies are reflected through the references to “Elegy” by a French composer J. Massenet (“Transformation”) and to vocal and instrumental performances of crossover music textes, decoding the collision of opera singer Ricardy (“The disappearance of Ricardy”). Ultimately, both of Gazdanov’s stories are considered to be a testimony to the acceptance of inevitability of human existence in two planes of being: ontologically possible and empirically given. The art strategy of audial writing has proven to be the most productive way to objectify this type of author’s consciousness in the writer’s early prose. The next stages of Gazdanov’s art system evolution are also marked by the author's great focus on the potential of audial and intermedial narration techniques. It offers the clear prospect of studying them as dynamical integrity.

DYNAMICS AND STABILITY: A LONG HISTORY FROM EQUILIBRIUM TO DYNAMICAL INTEGRITY

This work is aimed at reporting a personal, and thus partial, history of the dynamics and stability concepts within the framework of classical mechanics. The idea is to introduce these concepts without using mathematics and formula, but rather through practical and clear examples. For this purpose, it has been chosen to take in consideration some simple dynamic phenomena that we are used to live with, but that are able to explain more complex concepts. The paper starts with a brief summary on equilibrium concept evolution, passes through stability problems and arrives to more advanced concepts, such as structural stability and dynamical integrity.

Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity profiles and integrity charts are drawn. The curves of constant percentage of integrity measure are detected, highlighting that they provide valuable quantitative information about the changes in the structural safety. Robustness as well as vulnerability to disturbances is examined. The practical range of existence of each branch is observed to be smaller, and sometimes remarkably smaller than the theoretical one. The issue of the dynamical integrity analysis in the AFM design is addressed, showing that these curves may be used to establish safety factors in order to operate the AFM according to the desired outcome, depending on the expected disturbances. Physical meaning and practical relevance of the nonlinear phenomena in the AFM engineering design are discussed.

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics

The dynamical integrity, a new concept proposed by J.M.T. Thompson, and developed by the authors, is used to interpret experimental results. After reviewing the main issues involved in this analysis, including the proposal of a new integrity measure able to capture in an easy way the safe part of basins, attention is dedicated to two experiments, a rotating pendulum and a micro-electro-mechanical system, where the theoretical predictions are not fulfilled. These mechanical systems, the former at the macro-scale and the latter at the micro-scale, permit a comparative analysis of different mechanical and dynamical behaviours. The fact that in both cases the dynamical integrity permits one to justify the difference between experimental and theoretical results, which is the main achievement of this paper, shows the effectiveness of this new approach and suggests its use in practical situations. The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course: it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy (science); for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay up in the memory whole, as it finds it, but lays it up in the understanding altered and digested. Therefore, from a closer and purer league between these two faculties, the experimental and the rational (such as has never been made), much may be hoped. (Francis Bacon 1561–1626) But are we sure of our observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one's observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory . (Arthur Stanley Eddington 1882–1944)