Non Linear Dynamics

The purpose of the System Dynamics method is to study the relationship between structure and behavior in non-linear, dynamic systems. In such systems, the significance of various structural components to the behavior pattern exhibited, changes as the behavior unfolds. Changes in structural significance, in turn modifies that behavior pattern, which, in turn, feeds back to change the relative significance of structural components. We develop a mathematical framework within which we can study the characteristics of this feedback ...

We study a minimal, energy-accounting model of a driven-dissipative complex field that supports localized "energy patches". Within a single codebase we demonstrate: (E1.1) verified power balance; (E1.2) storage windows under gated drive; (E1.3) corridor transport with directed bias and a drain; (E1.4) controlled exchange across a bridge; (E1.5) robustness to additive and phase noise; (E1.6) a light optimization stub balancing storage and transport; and (E1.7) a simple kill-switch safety mechanism. We present generic formulas only; figures reference PNG outputs. Source tables/CSV are withheld.

This paper presents investigation on the effect of heavy axle loads on 2-span Reinforced Concrete Bridge superstructure using ANSYS workbench. The bridge is a link between the Nigeria export processing zone and Kano city. Damage to bridges is as a result of its repeated load-carrying capacity. The continuous flow of automobiles results in degradation and subsequent decline in the mechanical properties of the deck, leading to reduced reliability over an extended period. This research employed a relatively cost effective numerical approach to evaluate the possible damage accumulated and finite element model (FEM) of the bridge deck was developed based on preliminary calculations using information gathered from built drawings which help to predict the deterioration rate of the superstructure using simulation capability of ANSYS 2018. A single span of 16m by 8m width was isolated for a detailed structural analysis. The bridge 3D-geometry and material properties were modeled in ANSYS with calibration from CSiBridge v17 program and simulated in accordance with "British Code of Practice for Highway Bridges (BS 5400). At serviceability, the bridge maximum deflections at deck using ANSYS and CSI Bridge were 1.07.mm to 2.6mm and 1.1mm to 3mm respectively while at deck/girder were between 8.179mm to 11.673mm and 5mm to 11.1mm simulations respectively and values are within the acceptable range of span800-span1200mm or (13.33-20mm). The deck service stresses were found to be within the endurance Stress e (2-3.5)N/mm2 defined by the materials data. This study provides valuable scientific and practical outcomes that can be utilized in the design and operation of bridge structures, contributing to the development of infrastructure and ensuring the safety of transportation systems. The use of ANSYS software in the analysis process enhances the accuracy, and efficiency of the research, further emphasizing its relevance in the analysis of bridge.

We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.

In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control.

Dams are often subjected to earthquakes due to their localization in seismic zones. So, their behavior must be studied carefully. In this study, a concrete dam is studied taking into account the soil-fluid-structure interaction. The study is conducted using a non-linear analysis for finite element model. The dam of Oued el Fodda (Algeria) is taken as an example to apply the developed model. Two earthquakes were considered Kocaeli Izmit (1999) and Northridge (1994) and the obtained displacements and stress are compared.

Duffing oscillator with delayed feedback is widely used in engineering. Chaos in such system plays an important role in the dynamic response of the system, which may lead to the collapse of the system. Therefore, it is necessary and significant to study the chaotic dynamical behaviors of such systems. Chaotic dynamics of the Duffing oscillator subjected to periodic external and nonlinear parameter excitations with delayed feedback are investigated both analytically and numerically in this paper. With the Melnikov method, the critical value of chaos arising from heteroclinic intersection is derived analytically. The feature of the critical curves separating chaotic and nonchaotic regions on the excitation frequency and the time delay is investigated analytically in detail. Under the corresponding system parameters, the monotonicity of the critical value to the excitation frequency, displacement time delay, and velocity time delay is obtained rigorously. The chaos threshold obtained by the analytical method is verified by numerical simulations.

In order to study the dynamic response of historical masonry structures, a scaled down brick masonry model constructed in civil engineering department at Baghdad University to simulate a part of a real case study, which is Alkifil historic minaret. Most of the previous researches about masonry structures try to understand the behavior of the masonry under seismic loading by experimental and numerical methods. In this paper, the masonry units (bricks) simulated in scale (S= 1/6) with the exact shape of the prototype bricks. Cementitious tile adhesive was selected to be the mortar for the modeling. The height of the model designed to be 1.5 m with a 0.5 m diameter. Detailed construction steps were presented in this paper. Experts built the model with high accuracy. A shaking table and other dynamic testing facilities were used at the University of Baghdad. The model was tested using the time-compressed El Centro 1940 NS earthquake at different amplitudes. The first ground motion of (PGA= 0.05g) which considered as weak ground motion was used to check the adequacy of the conventional behavior of the masonry model and the limit of the elastic behavior of the model during weak earthquakes. Moderate ground motion (PGA=0.15g) was performed to investigate the response of the model with minor to moderate damages. The severe ground motions were not appropriate to use in such circumstances because of the possibility to overturn the model. The experimental results showed very adequacy of the model to withstand the weak and moderate earth motion with no observed cracks.

This paper presents a novel conjecture connecting the Hausdorff dimension of the energy spectrum in the Almost Mathieu Operator (AMO) to the irrationality measure of the magnetic flux parameter. Building upon the foundational work on quasi-periodic systems and the proven results regarding the Cantor set structure of the spectrum at critical coupling, we propose a stratified relationship D(σ(H_{α,2,θ})) = 1β(μ(α)) • ε(α), where β(μ(α)) is an irrationality scaling function and ε(α) represents fine-structure corrections based on continued fraction properties. This conjecture suggests that the fractal dimension of the quantum spectrum is fundamentally determined by the number-theoretic classification of the flux parameter α, with quadratic irrationals yielding D ≈ 0.85, cubic algebraic numbers giving D ≈ 0.92, and Liouville numbers approaching D → 1⁻. The proposed framework unifies concepts from Diophantine approximation theory, fractal geometry, and quantum mechanics, offering new insights into the metalinsulator transition in quasi-periodic systems. We provide detailed numerical testing protocols, theoretical justifications based on renormalization group theory, and discuss potential applications in condensed matter physics and quantum chaos.

Pavement performance evaluation is one of the most important steps of the pavement management system. It consists of identifying pavement condition according to various distresses occurs in the pavement surface. Data collection in performance assessment of road is done in several ways. An attempt has been made to address the problem and a new formalism is proposed for performance assessment of flexible pavements. Vagueness in the perception of expert for performance assessment of pavement based on techno-scientific parameters in linguistic terms for the domain base usage coupled with impression in parametric data calls for the application of fuzzy modeling. For this study fuzzy evidence theory weightage method "Dempster's Shafer's (D-S)" is applied to determine the Pavement Condition Distress Index (PCDI) of flexible pavement. D-S theory provides a designed framework to overcome the risk of uncertainty and ignorance. For the assessment of pavements five major structural indicators like longitudinal cracks, transverse cracks etc. and eleven major functional indicators like potholes, rutting, patching etc. are considered. Expert opinion is taken from the experts who are involved in the field of transportation engineering. Questionnaire Survey methodology has been adopted for the collection of experts opinions. Five linguistic terms are used for the same, which are, 'Very important', 'Important', 'Average', 'Less important' and 'Not Important'. Based on PCDI, Pavement Condition Index (PCI) is calculated. The rating of flexible pavements is also done based on PCI. For the application of the model, five road segments of MIDC Chakan, Pune area is considered. PCI of all the road segments is determined by using the stated index. Based on PCI value, road segment 1 rated 5 with less PCI value and road segment 4 rated 1 with high PCI value. The defined method is also compared with the rating system given in Indian Road Congress (IRC-82-2015).

The electricity transmission systems are an important lifeline for modern societies. They are used for overhead power lines as supporting structures. Transmission towers are designed to meet electrical and structural requirements. They are designed according to the weight of conductors and environmental effects such as wind and ice loads. They also considered other extraordinary stresses such as cable breakage and ice-breaking effects. Because of a common perception that transmission line (TL) towers show low sensitivity to earthquakes, the effects of the earthquake in TL tower construction are not considered. For this reason, TL towers are investigated with regard to the seismic performance in this study. The principal objectives of this research are: i) to assess the sensitivity of typical TL towers to earthquake loads, ii) to retrofit an existing steel lattice tower using a new section Centre To Center (CTC). In this study, a finite element model of a representative 154 KV transmission tower in Turkey was performed using a set of 10 recorded earthquake ground movements. The four-legged square TL tower has been analyzed and designed for Turkey, Eskisehir seismic zone considering 42.95 m height using finite element (FE) software. Therefore, a new section Centre To Center (CTC) type has been designed and the failed sections have been replaced with a designed section using the SAP2000 section designer. The results show that the load of failure increased after retrofitting. The retrofitting method was effective and easily conducted in fields.

We report on a paradoxical migration mechanism in a microstructured lab-on-a-chip environment. The phenomenon is based on a subtle interplay between Brownian motion (thermal noise), a periodic and symmetric microstructure, and a biased AC electric field. The resulting non-linear dynamics far from thermal equilibrium gives rise to absolute negative mobility, i.e. a migrational transport, which is -both for negative and positive bias -always opposite to the net acting force, in very good agreement between experiment and theory.

Understanding the relationship between topology and dynamics of transcriptional regulatory networks in mammalian cells is essential to elucidate the biology of complex regulatory and signaling pathways. Here, we characterised, via a synthetic biology approach, a transcriptional positive feedback loop (PFL) by generating a clonal population of mammalian cells (CHO) carrying a stable integration of the construct. The PFL network consists of the Tetracyclinecontrolled transactivator (tTA), whose expression is regulated by a tTA responsive promoter (CMV-TET), thus giving rise to a positive feedback. The same CMV-TET promoter drives also the expression of a destabilised yellow fluorescent protein (d2EYFP), thus the dynamic behaviour can be followed by time-lapse microscopy. The PFL network was compared to an engineered version of the network lacking the positive feedback loop (NOPFL), by expressing the tTA mRNA from a constitutive promoter. Doxycycline was used to repress tTA activation (switch off), and the resulting changes in fluorescence intensity for both the PFL and NOPFL networks were followed for up to 43 h. We observed a striking difference in the dynamics of the PFL and NOPFL networks. Using non-linear dynamical models, able to recapitulate experimental observations, we demonstrated a link between network topology and network dynamics. Namely, transcriptional positive autoregulation can significantly slow down the ''switch off'' times, as comparared to the non{autoregulatated system. Doxycycline concentration can modulate the response times of the PFL, whereas the NOPFL always switches off with the same dynamics. Moreover, the PFL can exhibit bistability for a range of Doxycycline concentrations. Since the PFL motif is often found in naturally occurring transcriptional and signaling pathways, we believe our work can be instrumental to characterise their behaviour.

The Atlantic Coast of southwestern Namibia is renowned for its Pliocene to Holocene diamondiferous deposits, which contributed more than 63 million carats of diamonds to the global market. A continuum of fossil shoreline deposits associated with barriers to linear and pocket beaches stretches over circa 110 km in length. Of these, the most highly economic are the fossil linear and pocket beach deposits that are preserved over highly competent Proterozoic bedrock. Potholes and gullies, the prominent bedrock-trapsite features, have controlled diamond concentration. By contrast, the barrier shorelines that developed on unconsolidated fluvial and marine sediments at a palaeo-river mouth are less productive. Here, trapsites are absent and diamond accumulation and retention occurred via interstitial trapping in a coarse gravel framework under highly energetic littoral settings. It therefore follows that diamond enrichment is governed by the sedimentological characteristics of the gravel allied to the dynamics of their depositional environments. We examine the relationship of diamond enrichment with the littoral processes at an environmental and subenvironmental level of a latest Pliocene/earliest Pliocene gravel barrier beach complex (BBC). Results show variability in both diamond concentrations and sizes across the barrier that commensurate with a diversity of morpho-sedimentary dynamics. The study, a first of its kind, provides insights into the diamond enrichment of a BBC. It demonstrates how detailed sedimentological reconstruction of the barrier environments can improve the exploration efficacy of such diamond-bearing littoral placers.

Agradeço primeiramente a Deus, que sempre escuta as minhas orações e preces, concedendo-me força e sabedoria para superar os momentos difíceis e guiando-me por caminhos de paz. Ao meu orientador Prof. Dr. Carlos Eduardo Nigro Mazzilli, por todo o incentivo, ensinamento, confiança, apoio, compreensão, inspiração e, principalmente, por me apresentar um novo e fascinante mundo dinâmico. À Escola Politécnica, por me acolher como aluno e propiciar um ambiente estimulante ao ensino e à pesquisa. Ao Prof. Guilherme Franzini, por todo o apoio no desenvolvimento das rotinas numéricas, pelas dúvidas sanadas e pelas valiosas contribuições ao longo do desenvolvimento deste trabalho. Ao amigo Fábio Rizza, pelo esforço despendido na comparação e compreensão dos resultados obtidos por meio dos modelos elaborados. Ao Núcleo Projetos e Consultoria, pelo tempo cedido para a realização desse trabalho; e aos meus colegas de profissão, pelo auxílio e apoio. Aos amigos da VLB Engenharia, em especial, à engenheira Flávia Carvalho Carreira, pelo conhecimento transmitido no início de minha formação profissional; e aos amigos Richard, Paloma, Silvia, Paula e Filipe, pelas ricas discussões técnicas e pela amizade que se mantém viva ao longo desses anos. Aos professores da Escola de Engenharia da Universidade Federal de Minas Gerais, Dr. Gabriel de Oliveira Ribeiro e Dr.ª Sofia Maria Carrato Diniz, pelo incentivo à pesquisa e por acreditarem em meu potencial. À minha avó Therezinha (in memoriam) e à minha mãe Carla, que em meio às dificuldades sempre se mantiveram em pé, alimentando seus sonhos e esperanças. Ao grande companheiro e amigo Maykon Diego, por toda sua paciência, compreensão, afeto e carinho nos momentos difíceis e prazerosos dessa caminhada. Aos amigos Fernando, Wanderson e Mariana, pela amizade que ultrapassa a distância e o tempo; e a todos aqueles que propiciaram momentos de alegria e souberam compreender a ausência. "O cientista não estuda a natureza porque ela é útil; ele a estuda porque se deleita nela, e se deleita nela porque ela é bela. Se a natureza não fosse bela, não valeria a pena ser conhecida, e se não valesse a pena ser conhecida, a vida não valeria a pena ser vivida."

This article presents a conceptual analogy between the mathematical curiosity of Kaprekar's constant (6174) and the emergence of consciousness. It posits that the iterative process of reaching this constant serves as a model for how the brain's vast, parallel processing converges into a singular, stable state of awareness.

The Kaprekar routine, which involves repeatedly rearranging a four-digit number's digits into descending and ascending orders and subtracting them, is framed as a deterministic, self-organizing system. The initial number represents raw, unprocessed sensory and cognitive data. The iterative algorithm mirrors the brain's process of differentiation and integration, as described in frameworks like Global Workspace Theory (GWT) and Integrated Information Theory (IIT). The inevitable convergence on the fixed-point attractor, 6174, is analogous to achieving a stable, unified conscious state.

The analogy extends to states of unconsciousness and pathology. The exception of "repdigits" (e.g., 3333), which collapse to zero, models the low informational complexity of deep sleep or coma. Cyclical patterns found with other digit lengths are compared to recurring mental states like rumination or mood disorders.

Finally, the article critiques its own analogy by addressing the "hard problem of consciousness." It concludes that the Kaprekar routine is a purely syntactic process, manipulating symbols without semantic understanding, much like the scenario in Searle's Chinese Room argument. While the model effectively illustrates the dynamics of achieving a stable conscious state (the "easy problems"), it cannot explain subjective experience, or qualia. The analogy thus serves as a conceptual tool to clarify the limits of functionalist explanations of the mind.

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane's bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment may already be a part of other lateral-directional stability derivatives, most probably in dihedral effect. Nevertheless, the overbanking tendency may also be induced by propulsive and/or gyroscopic moments, airplane and flight control rigging problems, human factors, and improper piloting techniques. Straightforward explanation of the overbanking tendency is based on the asymptotic spiral divergence lateral-directional mode, which is very common in many FAR 23 airplane designs. The full nonlinear stability model, which may include coupling of longitudinal, lateral, and directional motion in steep turns at high angles of attack and including propulsive moments, may be required to make the final judgment about the existence of the overbanking tendency. A thorough review of airplane turning performance in horizontal plane is presented.

This paper proposes a new hypothesis that connects energy and motion. It states that the change in energy within a system is directly proportional to the change in its speed. This approach offers an alternative way to think about the flow of energy and the passage of time, potentially linking mechanics, thermodynamics, and relativity under a common view.

This paper proposes a new hypothesis that connects energy and motion. It states that the change in energy within a system is directly proportional to the change in its speed. This approach offers an alternative way to think about the flow of energy and the passage of time, potentially linking mechanics, thermodynamics, and relativity under a common view.

This paper proposes a new hypothesis that connects energy and motion. It states that the change in energy within a system is directly proportional to the change in its speed. This approach offers an alternative way to think about the flow of energy and the passage of time, potentially linking mechanics, thermodynamics, and relativity under a common view.

In a series of papers, Degtyarev and Reed have presented the theory and provided the results from an autoregressive model for representing a seaway—at a point in space, over a line and over a plane, all as a function of time (1-D, 2-D & 3-D, respectively). In several other papers, Degtyarev and Gankevich have provided the theory for a technique for efficiently computing the velocity potential beneath a prescribed 1-D or 2-D surface, varying with time. Together this series of papers provides the information needed to compute the fully nonlinear hydrostatic and Froude-Krylov pressures under a seaway in an efficient manner without having to be concerned with the computing-time constraints imposed by the use of a Fourier series representation of a seaway imposed by the use of a Longuet-Higgins model. The next step is to apply these models in a seakeeping code so that the practical aspects of using these appealing theoretical approaches can be assessed. This paper provides a very brief d...

In this paper we propose a classification scheme to isolate truly benign tumors from those that initially start off as benign but subsequently show metastases. A non-parametric artificial neural network methodology has been chosen because of the analytical difficulties associated with extraction of closed-form stochastic-likelihood parameters given the extremely complicated and possibly non-linear behavior of the state variables. This is intended as the first of a three-part research output. In this paper, we have proposed and justified the computational schema. In the second part we shall set up a working model of our schema and pilot-test it with clinical data while in the concluding part we shall give an in-depth analysis of the numerical output and model findings and compare it to existing methods of tumor growth modeling and malignancy prediction.

In this paper we propose a classification scheme to isolate truly benign tumors from those that initially start off as benign but subsequently show metastases. A non-parametric artificial neural network methodology has been chosen because of the analytical difficulties associated with extraction of closed-form stochastic-likelihood parameters given the extremely complicated and possibly non-linear behavior of the state variables. This is intended as the first of a three-part research output. In this paper, we have proposed and justified the computational schema. In the second part we shall set up a working model of our schema and pilot-test it with clinical data while in the concluding part we shall give an in-depth analysis of the numerical output and model findings and compare it to existing methods of tumor growth modeling and malignancy prediction.

In a previous study, we showed that the 1992 m en' s world record running times in the 100 m to 200 km could be represented accurately by the equation T = cD n , where T is the calculated record time for distance D , and c and n are positive constants. Here, we extend that to cover the years 1925± 65 at 10-year intervals and 1970± 95 in 5-year intervals for distances of 100 m to 10 km. Values of n for all years lie along a straight line with a small negative slope. A regression analysis yields an equation for values of n covering the period 1925± 95. Values of c from 1925 to 1995 were W tted by a quadratic equation. These two equations deW ne a surface in threedimensional space á log(T ), log(D), dateñ for all men' s world record runs over the 70-year period for distances of 100 m to 10 km. We also demonstrated previously that event times, t, do not scatter randomly with respect to the values of T but form a consistent pattern about the straight lines in log(T ) versus log(D ) plots. In this study, we show that the pattern of (t -T )/t as a function of date has remained constant for the past 70 years.

We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time stepping schemes of approximation for fractional differential operators. For that purpose, we use criteria for chaos of Toeplitz operators in Lebesgue spaces of sequences. Surprisingly, this characterization is proved to be -in some cases -dependent of the fractional order of the operator and the step size of the scheme. The study of discrete nonlocal operators, having fractional order operators as a prototype, is a fashionable area of study nowadays. As it has been recently demonstrated, systems with this property can be used to develop data encryption algorithms. The basis for such property is the chaotic behavior of the systems under consideration. With this motivation, we investigate necessary and sufficient conditions for chaos, uniquely based on the available data of nonlocal operators arising in numerical analysis, namely, the fractional order and the step size. We have success in our investigation and having our new findings somewhat surprising: We find that for the dual of the operator that defines the second order backward fractional difference scheme chaos is dependent on the step size but not on the fractional order and, by contrast, in case of the fractional Crank-Nicholson scheme chaos is dependent on the step size and the fractional order. Consequently, our new findings have ultimate importante in the development of algorithms based on the mentioned schemes of approximation, among others, which are also analyzed in the present research.

We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time-stepping schemes of approximation for fractional differential operators. For that purpose, we use criteria for chaos of Toeplitz operators in Lebesgue spaces of sequences. Surprisingly, this characterization is proved to be—in some cases—dependent of the fractional order of the operator and the step size of the scheme.

I present a resolution to the Navier-Stokes existence and smoothness problem by extending classical fluid dynamics into a fifth-dimensional temporal manifold, known as the Chronoflux framework. This theory introduces a hydrodynamic flow of time itself, governed by temporal differential inertia and quantum informational resistance. We demonstrate that classical 3D singularities arise from an incomplete projection of higher-dimensional dynamics and show, through rigorous derivation, that smooth solutions always exist within the extended manifold. All relevant mathematical structures and derivations are included, fulfilling the Clay Mathematics Institute's requirement for a complete resolution.

Tuning fork experiments at the undergraduate level usually only demonstrate a tuning forks linear resonance. In this paper, we introduce an experiment that can be used to measure the nonlinear tuning curve of a regular tuning fork. Using double-grating Doppler interferometry, we achieve measurement accuracy within ten microns. With this experiment setup, we observe typical nonlinear behaviors of the tuning fork such as the softening tuning curve and jump phenomena. Our experiment is inexpensive and easy to operate. It provides an integrated experiment for intermediate-level students and a basis for senior research projects.

distinction between changes in the form of the production function corresponding to innovation, and shifts along the production function corresponding to factor substitution, does not preclude that the underlying dynamics interact. In an evolutionarily complex system, such interactions are expected: they lead to non-linear terms in the model, and therefore to stabilization and self-organization in addition to selection and variation. Relatively simple simulations enable us to specify various concepts used in "evolutionary economics" in terms of nonlinear dynamics. While a technological trajectory can be considered as a stabilization in a (distributed) environment, a technological regime can be defined as a next-higher-order globalization in a hyper-space. A regime is able to restore its order despite local disturbances, for example by the political system. Technology policies may be effective at the level of the (sub-)systems if they provide the relevant agents with room for "creative destruction" of the globalized hyper-systems. Implications for firm behaviour and innovation policies are elaborated.

Based on a microscopic many-particle theory we study the amplification of polaritons in a multiple-quantum-well resonant photonic crystal. For the Bragg-spaced multiple quantum wells under investigation we predict that in a typical pump-probe setup four-wave mixing processes can lead to an unstable energy transfer from the pump into the probe and the background-free four-wave mixing directions. We find that under certain excitation conditions this phase-conjugate oscillation induced instability can lead to a large amplification of the weak probe pulse.

The main goal of this paper is to present experimental and numerical studies of dynamic axial crushing of thin-walled monotubal and bitubal foam-filled cylindrical sections. Design/methodology/approach: Dynamic tests were performed on empty as well on foam-filled specimens. The effect of filling the specimens with different density polyurethane foams was studied as well. The explicit dynamics non-linear finite element code PAM-CRASH™ was used to simulate the crushing of columns. Findings: The influence of fillers on energy absorption and behavior of circular thin-walled monotubal and bitubal arrangements was examined. Three main collapse modes were identified for the crushed samples, i.e. compound diamond (asymmetric), concertina (axisymmetric) and mixed mode fold formations. Research limitations/implications: Further investigations concerning energy absorption of axially crushed monotubal and bitubal sections should be done. The influence of cross-section, foam density, impact velocity and other parameters should be examined more in details. Practical implications: The polyurethane foams turned out to be a significant factor positively influencing the energy absorption capability and so by application in the longitudinal members of cars frame improving passengers' safety. Originality/value: Further investigations concerning compressing of foam-filled monotubal and bitubal sections were presented. The results achieved from conducted tests proved the dependence of energy dissipation on application of filling materials and composite structures.

Quantum mechanics is empirically unmatched but conceptually opaque. Fold Theory for Quantum Mechanics (FTQM) offers a structural reinterpretation: it retains quantum formalism but recasts its ontology through recursive coherence. Where conventional interpretations debate wavefunction collapse, FTQM reframes superposition as unresolved constraint descent, and measurement as structural resolution across morphic depth. Decoherence arises from recursive shear, not environmental disturbance. Probability reflects stabilization frequency within a generative coherence manifold.

This framework does not evade Gödel's incompleteness-it accepts it as a feature, proposing physics as an open system of coherence constraints rather than a closed set of axioms. FTQM offers a structural foundation compatible with standard predictions but opens pathways toward postquantum computation, context-sensitive experimental architectures, and a recursive ontology where causality and computation co-emerge.

Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the tr...

In general, the oscillator is a device that used in most circuits and system of electronics, electrical, and telecommunications. There are several kinds of oscillator contingent on frequency band use in a submission such as microwave, audio, and radio frequency. LC oscillator is one of the greatest mutual categories of oscillators, the applications of this oscillator was seemed to be increasing in modern devices, for actual high and very high frequencies to meet the speedy growth of progressive knowledge. That can be secondhand for radio frequency (RF), its productivity signal is frequently applied at the basis of radio communication classification in furthermost applications. In this paper, a designed Colpitts oscillator is covered from voltage amplifier with LC container. This strategy is done by two approaches. Primarily, is approved out exploitation hypothetical scheming. The subordinate is supported out exploitation imitation (Multisim 13). There are two proposal types of circuits the first for generate signal frequencies 0.5MHz,1MHZ,10MHz,20MHz,50MHz &100MHz, the second for generate signal frequencies 4.963MHZ, 5.031MHZ, and 5.756MHz respectively. The consequence is realized to be very hopeful.

This material is based upon work supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement No. 1852977. RJL acknowledges support from NASA’s Living With a Star Program. We thank Phil Scherrer and J. Todd Hoeksema for their assistance with, and discussions on, the Wilcox Solar Observatory data, and Dipankar Bannerjee for assistance with the Kodaikanal Observatory data.

The objective of this study is to evaluate the dynamic structural performance of bridge structure under moving load by determining natural frequency, loaded vibration frequency, loaded dynamic displacement, loaded dynamic acceleration, and loaded dynamic velocity. In this study, the dynamic analysis is used to discover dynamic responses. This type of analysis is applied on the design loaded stage which it means that the bridge structure in the initial condition (before traffic passes on bridge) with grade of concrete (compressive strength) is 50MPa. CSI-Bridge Ver. 24 is adopted in the bridge structure model for dynamic analysis. According to the results of the dynamic analysis, the magnitude of natural vibration frequency is 2.97Hz and the higher value of loaded vibration frequency is 3.371Hz in the center of span No.3 (middle of bridge), and the average magnitude of bridge loaded vibration frequency is 3.004Hz. Therefore, the bridge structure experiences loaded dynamic vibration because the natural vibration frequency is lower than the frequency of loaded vibration. indicating that the bridge's rigidity has to be improved. The dynamic structural performance of bridge structures is significantly impacted by the other dynamic responses, such as dynamic displacement, dynamic acceleration, and dynamic velocity, which are all specified and the higher magnitude of downward loaded dynamic displacement is acted in span No.1 which is-0.00778m and for upward dynamic displacement, the higher value is 0.00115m in the span No.1 and lower value is 00055m within span No. 2. This study recommended that to strengthen the bridge structure to reduce the dynamic effect under traffic loads.

High energy solar flares and coronal mass ejections have the potential to destroy Earth's ground and satellite infrastructures, causing trillions of dollars in damage and mass human suffering. This would lead to food shortages and crippled emergency response capabilities. A solution to this impending problem is proposed herein using satellites in solar orbit with built-in machine learning capability that continuously monitor the Sun. They will use machine learning to calculate the probability of massive solar explosions from the remote sensing data, then signal defence mechanisms that can mitigate the threat. This paper reports the results from a survey of machine learning models using open-source solar flare prediction data. The rise of edge computing supports machine learning hardware placed on the same satellites as the sensor arrays, saving critical transmit time across the vast distances of space. A system of systems approach will allow enough warning for safety measures to be enacted, thus mitigating the risk of disaster.

The purpose of the System Dynamics method is to study the relationship between structure and behavior in non-linear, dynamic systems. In such systems, the significance of various structural components to the behavior pattern exhibited, changes as the behavior unfolds. Changes in structural significance, in turn modifies that behavior pattern, which, in turn, feeds back to change the relative significance of structural components. We develop a mathematical framework within which we can study the characteristics of this feedback ...

The nonlinear dynamics o f circular cylindrical shells under combined axial static and periodic forces are experimentally investigated. The goal is to study the dynamic scenario and to analyze non-linear regimes. The linear behavior under static preload is analyzed by means o f the usual modal testing techniques. The complex dynamics arising when a periodic axial load excites the first axisymmetric mode are analyzed by means o f amplitude frequency diagrams, waterfall spectrum diagrams, bifurcation diagrams o f Poincare maps, time histories, spectra, phase portraits.

In this paper, the results of an experimental campaign focused on the vibrations of shells are presented. More specifically, the goal is to investigate the effect of thermal gradients across the shell thickness on the nonlinear dynamics. The shell is made of polymeric material and an aluminum mass is clamped on one end of the shell; the other shell end is clamped to an electrodynamic shaker, which provides a base harmonic excitation. Tests are performed in a controlled environment where a thermal gradient on the shell thickness is generated by means of a climatic chamber and an internal cartridge heater. Different temperature gradients and base excitation levels have been considered. The nonlinear dynamic scenario is analyzed through amplitude–frequency diagrams, bifurcation diagrams, waterfall diagrams, time histories, Fourier spectra, phase portraits, and Poincaré maps. Results show a strong effect of the temperature on the dynamic response of the shell: subharmonic, quasi-periodi...

In this paper the nonlinear dynamics of circular cylindrical shells under axial static (compressive) and periodic resonant loads have been experimentally investigated, the goal is to study the dynamic scenario and to analyze nonlinear regimes. A special test rig has been developed for the experiment in order to apply a static axial load combined with a dynamic axial load. The setup allows for investigating the linear behavior under static preload by means of the usual modal testing techniques; moreover, it allows for analyzing the nonlinear response which occurs when the dynamic axial load is periodic and gives rise to complex resonances. The complex dynamics, arising when a periodic axial load excites the asymmetric (shell like) modes, are analyzed by means of amplitude frequency diagrams, waterfall spectrum diagrams, bifurcation diagrams of Poincaré maps; a deep analysis of time histories, spectra, phase portraits and Poincaré maps completes the study of the complex dynamic scenario.

Classical Mechanics by Herbert Goldstein is a foundational graduate-level textbook that provides a rigorous and comprehensive treatment of classical mechanics, the study of the motion of physical systems under the influence of forces. The book covers a wide range of topics including Newtonian mechanics, Lagrangian and Hamiltonian formulations, central force motion, rigid body dynamics, small oscillations, canonical transformations, Hamilton–Jacobi theory, and an introduction to relativistic mechanics and nonlinear dynamics.

Goldstein emphasizes formal mathematical methods and principles of theoretical physics, making the text suitable for students seeking a deeper understanding of the analytical framework underlying classical physics. The book is known for its clear exposition, challenging problem sets, and its role as a bridge to more advanced topics in modern physics and quantum mechanics.

In today's complex web of socio-economic, political and environmental changes, natural sciences' approaches may offer insufficient understanding of the dynamics underlying socio- ecological systems. Local knowledge is an important key to understanding pastoralist strategies of resource management. It is particularly interesting to investigate how local knowledge is produced and used in a highly unpredictable system, characterized by non-linear dynamics. Pastoralism is the dominant form of land use and economy in the arid north-western parts of Namibia. The sustainable management of natural resources is therefore important to guarantee future livelihoods in this region.

This document marks the empirical closure of the RCFT/ULRC protocol chapter, presenting the definitive set of analytic invariants, empirically calibrated thresholds, and regime assignment logic for collapse diagnosis and repair. All canonical operators—symbolic drift, recursive fidelity, entropy, curvature, reentry delay, and composite integrity—are formally defined and empirically validated, supporting real-time regime detection and audit across scientific, technological, and symbolic fields. Audit trail protocols, regime assignment tables, and explicit ethical safeguards are embedded throughout. This closure document establishes the canonical reference for traceability, reproducibility, and additivity in RCFT/ULRC regime assignment and protocol implementation, and serves as the foundational endpoint for this stage of theory and practical deployment  .

In the last years, there is an increasing interest in nonsmooth system dynamics motivated by different applications including rotor dynamics, oil drilling and machining. Besides, shape memory alloys (SMAs) have been used in various applications exploring their high dissipation capacity related to their hysteretic behavior. This contribution investigates the nonlinear dynamics of shape memory alloy nonsmooth systems considering a linear oscillator with a discontinuous support built with an SMA element. A constitutive model developed by Paiva et al. [Paiva A, Savi MA, Braga AMB, Pacheco PMCL. A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 2005;42(11-12):3439-57] is employed to describe the thermomechanical behavior of the SMA element. Numerical investigations show results where the SMA discontinuous support can dramatically change the system dynamics when compared to those associated with a linear elastic support system. A parametric study is of concern showing the system behavior for different system characteristics, forcing excitation and also gaps. These results show that smart materials can be employed in different kinds of mechanical systems exploring some of the remarkable properties of these alloys.

We study the modulational instability in discrete lattices and we show how the discreteness drastically modifies the stability condition. Analytical and numerical results are in very good agreement. We predict also the evolution of a linear wave in the presence of noise and we show that modulational instability is the first step towards energy localization.