Fractal Paradigm Research Articles

Семиодинамика метафоры (на материале медицинского английского языка)

The aim of the study is to prove the metaphoric character of the terminological system of English biological and medical scientific discourse. The scientific novelty of the work lies in the author’s approach to the analysis and interpretation of the ‘host’ metaphor from the position of the fractal paradigm in metaphorology. As a result of the study, it has been revealed that the primary name of the word ‘host’ contained a positive heuristic based on creating an image of a hospitable host in order to obtain benefits. But the evolution of the name has led to a change of positive heuristics to a negative one and a change in the stylistic significance of the metaphor. The initially occasional metaphor became a trite one and contributed to the emergence of the medical and biological term. It has been found that the semiodynamics of the word ‘host’ affects the change in the stylistic significance of the metaphor and manifests itself in metaphorical mapping when the concepts FRIEND and ENEMY, FRIEND and FOE interact in the cognitive space of the COEXISTENCE concept. It has been found and proved that the evolution of the metaphor, fractal in nature, manifests itself in the transfer of the same name from the HOSPITALITY concept to the DAMAGE concept.

A novel computing method for the fractal paradigm of straight fin energy problem arising in the heat transfer

A novel computing method for the fractal paradigm of straight fin energy problem arising in the heat transfer

Фрактальные приложения радиоэлектроники как фрактальная инженерия

The use of the fractal paradigm is presented - the main directions for introducing textures, fractals, fractional operators, dynamic chaos and methods of nonlinear dynamics for the design and creation of real technical projects in radio electronics - fractal radio systems, taking into account the hereditarity, non-Gaussianity and scaling of physical signals and fields. The substantiation of the use of fractal-scaling and texture methods for the synthesis of fundamentally new topological texture-fractal methods for detecting signals in the space-time channel of scattering waves (a new type of radar) is discussed. It is shown that the use of fractal systems, sensors and nodes is a fundamentally new solution that significantly changes the principles of constructing intelligent radio engineering systems and devices. It is shown that the use of computational dielectric metasurfaces brings to a new level all the functional characteristics of a multifunctional system of topological texture-fractal processing of signals and fields in solving classical problems of detection, measurement, recognition and classification by intelligent radio engineering systems and devices. The concept of "fractal engineering" is introduced, the methodology of its use is discussed.

Prospects and Challenges of the Drug Delivery Systems in Endometriosis Pain Management: Experimental and Theoretical Aspects.

Endometriosis is considered a serious public health issue because of the large number of females affected by this illness. Chronic pain management in patients with endometriosis demands new strategies to increase the life quality of these patients. The development of drug delivery systems represents a new approach in pain treatment among endometriosis patients. Diclofenac sodium, one of the most utilized nonsteroidal anti-inflammatory drugs (NSAID), has its own limitations when being used in formulas such as oral, parental, or local applications. In this paper, a series of four drug release formulations based on chitosan, 2-hydroxy-5-nitrobenzaldehyde, and diclofenac sodium salt were prepared in view of the investigation of the drug release ability. The formulations were analyzed from a morphological and supramolecular point of view by scanning electron microscopy and polarized light microscopy. The in vitro drug release ability was investigated by mimicking a physiologic environment. A mathematical model, using the fractal paradigm of motion, is utilized to explain the behaviors of the drug delivery system presented in this paper. These results suggest a great potential of the proposed drug delivery system, based on chitosan and 2-hydroxy-5-nitrobenzaldehyde to improve the diclofenac sodium salt bioavailability, and it may represent a future treatment formula for endometriosis pain.

“Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm

Assimilating a complex fluid with a fractal object, non-differentiable behaviors in its dynamics are analyzed. Complex fluid dynamics in the form of hydrodynamic-type fractal regimes imply “holographic implementations” through velocity fields at non-differentiable scale resolution, via fractal solitons, fractal solitons–fractal kinks, and fractal minimal vortices. Complex fluid dynamics in the form of Schrödinger type fractal regimes imply “holographic implementations”, through the formalism of Airy functions of fractal type. Then, the in-phase coherence of the dynamics of the complex fluid structural units induces various operational procedures in the description of such dynamics: special cubics with SL(2R)-type group invariance, special differential geometry of Riemann type associated to such cubics, special apolar transport of cubics, special harmonic mapping principle, etc. In such a manner, a possible scenario toward chaos (a period-doubling scenario), without concluding in chaos (nonmanifest chaos), can be mimed.

Novel solitary wave solution of the nonlinear fractal Schrödinger equation and its fractal variational principle

PurposeThe nonlinear Schrödinger equation plays a vital role in wave mechanics and nonlinear optics. The purpose of this paper is the fractal paradigm of the nonlinear Schrödinger equation for the calculation of novel solitary solutions through the variational principle.Design/methodology/approachAppropriate traveling wave transform is used to convert a partial differential equation into a dimensionless nonlinear ordinary differential equation that is handled by a semi-inverse variational technique.FindingsThis paper sets out the Schrödinger equation fractal model and its variational principle. The results of the solitary solutions have shown that the proposed approach is very accurate and effective and is almost suitable for use in such problems.Practical implicationsNonlinear Schrödinger equation is an important application of a variety of various situations in nonlinear science and physics, such as photonics, the theory of superfluidity, quantum gravity, quantum mechanics, plasma physics, neutron diffraction, nonlinear optics, fiber-optic communication, capillary fluids, Bose–Einstein condensation, magma transport and open quantum systems.Originality/valueThe variational principle of the Schrödinger equation without the Lagrange multiplier method in the sense of the fractal calculus is developed for the first time in the literature to the best of the author's understanding.

Polymer Dynamics Through Group Invariance of SL(2R) - Type in a Fractal Paradigm

We analyze polymer dynamics in a fractal paradigm. Then, it is shown that polymer dynamics in the form of Schrödinger - type regimes imply synchronization processes of the polymers� structural units, through joint invariant function of two simultaneous isomorphic groups of SL(2R) - type, as solutions of Stoka equations. In this context, period doubling, damped oscillations, self - modulation and chaotic regimes emerge as natural behaviors in the polymer dynamics. The present model can also be applied to a large class of materials, such as biomaterials, biocomposites and other advanced materials.

Charged Particle Oscillations in Transient Plasmas Generated by Nanosecond Laser Ablation on Mg Target

The dynamics of a transient plasma generated by laser ablation on a Mg target was investigated by means of the Langmuir probe method and fractal analysis. The empirical data showcased the presence of an oscillatory behavior at short expansion times (<1 μs) characterized by two oscillation frequencies and a classical behavior for longer evolution times. Space- and time-resolved analysis was implemented in order to determine main plasma parameters like the electron temperature, plasma potential, or charged particle density. In the motion fractal paradigm, a theoretical model was built for the description of laser-produced plasma dynamics expressed through fractal-type equations. The calibration of such dynamics was performed through a fractal-type tunneling effect for physical systems with spontaneous symmetry breaking. This allows both the self-structuring of laser-produced plasma in two structures based on its separation on different oscillation modes and the determination of some characteristics involved in the self-structuring process. The mutual conditionings between the two structures are given as joint invariant functions on the action of two isomorph groups of SL(2R) type through the Stoler-type transformation, explicitly given through amplitude self-modulation.

Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma

An innovative theoretical model is developed on the backbone of a classical Lorenz system. A mathematical representation of a differential Lorenz system is transposed into a fractal space and reduced to an integral form. In such a conjecture, the Lorenz variables will operate simultaneously on two manifolds, generating two transformation groups, one corresponding to the space coordinates transformation and another one to the scale resolution transformation. Since these groups are isomorphs various types isometries become functional. The Lorenz system was further adapted to describe the dynamics of ejected particles as a result of laser matter interaction in a fractal paradigm. The simulations were focused on the dynamics of charged particles, and showcase the presence of current oscillations, a heterogenous velocity distribution and multi-structuring at different interaction scales. The theoretical predictions were compared with the experimental data acquired with noninvasive diagnostic techniques. The experimental data confirm the multi-structure scenario and the oscillatory behavior predicted by the mathematical model.

Fractal methods in intelligent technologies for processing large data streams

In this work a new approach to the construction of models and logic circuits of algorithms and procedures for information technology processing and analysis of big data streams within the fractal paradigm is describes. In this case, data streams are defined as information objects whose physical nature can be arbitrary. The information object is investigated apart from any model or scheme, the logical scheme of intellectual technology is built in the form of: facts, regularities and reality. Fractal methods form the framework of the logical, algorithmic and content essence of the approach. The basic premise of the approach is as follows. First, the processing and analysis of data stream to determine whether it forms a fractal structure and construct a phase portrait of data stream as an information object. Second, to distinguish the areas of fractal percolation and aggregation in the multifractal structure of the stream, the phase portrait is used. Third, to estimate the spatial and temporal scales of fractal percolation and aggregation processes.

On the separation of particle flow during pulse laser deposition of heterogeneous materials - A multi-fractal approach

The problem of plasma self-structuring during the pulse laser deposition of multicomponent materials is discussed from both theoretical and experimental perspectives. A non-differential mathematical model was used to build the set of equation to characterize a complex fluid, assimilated with the laser produced plasmas in the fractal paradigm. Numerical simulations regarding the flow of a fractal fluid were performed reflecting real multi-component plasmas. These revealed that the structuring of a fluid is strongly related to its fractality and thus to individual properties of its components. The theoretical results were confronted with experimental data regarding the flow of multi-component plasma in a fluid representation. The laser produced plasma was investigated by means of ICCD fast camera imaging and optical emission spectroscopy. The experimental results showcase a splitting process on the two main directions coupled with a separation of the ejected particles with respect to their excitation energy. Both theoretical and experimental data are in good agreement.

Fractal and topological sustainable methods of overcoming expected uncertainty in the radiolocation of low-contrast targets and in the processing of weak multi-dimensional signals on the background of high-intensity noise: A new direction in the statistical decision theory

The main purpose of this work is to interpret the main directions of radio physics, radio engineering and radio location in “fractal” language that makes new ways and generalizations on future promising radio systems. We introduce a new kind and approach of up-to-date radiolocation: fractal-scaling or scale-invariant radiolocation. The new topologic signs and methods of detecting the low-contrast objects against the high-intensity noise background are presented. It leads to basic changes in the theoretical radiolocation structure itself and also in its mathematical apparatus. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlie the scientific direction established by the author in Russia and all over the world for the first time ever.

Multifractal analysis of the earth oblateness and Length-Of-Day fluctuations

Geodynamic processes acting on the Earth’s system continuously modify the redistribution of the Earth’s mass. As a result, various inherent global physical parameters, including the gravitational field of the Earth and its variability, as well as the Earth’s rotation rate and variations often observed in Length-Of-Day (LOD), are affected. The Earth’s gravity field is described by a set of spherical harmonic functions derived from a combination of various satellite data as well as terrestrial observations. These functions act as proxy parameters that contribute towards our understanding of the dynamics of the Earth’s system. One of the most important spherical harmonic coefficients of the gravity field of the Earth is the even zonal harmonic coefficient J 2 . This coefficient is used to describe the Earth’s flattening due to mass distribution between the Earth’s Equator and the polar regions, and is therefore a measure of the Earth oblateness. The J 2 coefficient exhibits spatial-temporal variations which are often correlated with LOD variations. The aim of this contribution is to use the fractal nature of J 2 and LOD to demonstrate that their variability is not characterized by well-defined scales (of time) that play dominant roles, but rather involve all scales equally. Characterizing the variability of J 2 and LOD using the fractal paradigm will enhance our understanding of the complex geophysical processes of the Earth system.

Sustainable Fractal Manufacturing: A New Approach to Sustainability in Machining Processes

Over the last decades manufacturing industry alongside installations and activities have caused damage to the planet, society and ecosystem. This impact is characterized by spending energy and material resources, environmental degradation, destruction of ecosystems, loss on biodiversity, effects on public health, welfare and life quality. Actions [1] that have been carried out to mitigate this situation have increased the complexity in manufacturing processes. It is necessary to establish new models that reduce this complexity in design and management stage, and allow the development of task's manufacturing to promote sustainability in the processes involved, maintaining the technical, economic and quality feasibility. The aim of this work is to develop a manufacture model based on the Fractal Paradigm to manage and structure the manufacturing processes, including the sustainability as minimal complexity (or required complexity) in manufacturing systems and incorporating the new paradigms Green Manufacturing and Cleaner Production, taking into account the principles of Cradle to Cradle (C2C).

The Hidden Meaning of Planck’s Constant

A new cosmological paradigm based upon global discrete self-similarity proposes a radical revision in our understanding of atomic scale dynamics. The discrete fractal scaling of this paradigm predicts a very large and discrete scale-dependence for gravitational coupling constants. This alternative gravitational scaling leads to revised values for the Planck mass, Planck length and Planck time, which appear to be more unified and physically comprehensible than is the case with the conventional Planck scale values. The fundamental interrelationship of the revised Planck mass, the corrected gravitational constant for atomic scale systems, the reduced Planck's constant and the velocity of light suggests a hidden meaning for Planck's constant. Within the context of the discrete fractal cosmological paradigm, Planck's constant is revealed as the fundamental unit of gravitational action for atomic scale systems. Implications for atomic scale dynamics are briefly outlined.

A NEW CONCEPTUAL FRAMEWORK FOR ENVIRONMENTAL DECISION BASED ON FRACTAL PHILOSOPHY

The expression „environmental decision” cannot be explained or summarized by a simple formula containing all the ideas focused on it. This paper aims to develop a conceptual framework for environmental decision (at organizations level) using fractal paradigm philosophy in its construction, with the purpose to bring order and simplicity for this type of decision. The study is based on the analysis of several environmental documentations (existing at the level of large organizations located in the North Easter Region of Romania), discussions with specialists in the field, and literature review. The new conceptual framework for environmental decision brings a real and substantial contribution materialized in ordering the levels of different environmental “problems”, at organizational level, and implicitly the related environmental decisions. The need for this new theoretical framework results from the analysis of existing inconsistencies at organizations level regarding the environmental decisions. The inconsistencies are generated by an incorrect delimitation or even the absence of environmental responsabilities absolutely necessary for effective environmental decision making process, and not only. This conceptual framework developed as a support tool for environmental decision making is founded on multidisciplinary principles (fractal philosophy) as the first attempt of this kind retrieved so far in the literature of general environmental management.

The concept of fractal cosmos: III. Present state

This is the sequel to the previous accounts on the rise and development of the concept of fractal cosmos, up to year 2001 (Grujic 2001, 2002). Here we give an overview of the present-day state of art, with the emphasis on the latest developments and controversies concerning the model of hierarchical universe. We describe both the theoretical advances and the latest empirical evidence concerning the observation of the large-scale structure of the observable universe. Finally we address a number of epistemological points, putting the fractal paradigm into a broader cosmological frame.

Discreteness of spatial-temporal manifestations of solar activity and solar-terrestrial phenomena

The discreteness of the time series of the solar-related geophysical phenomena is justified. The balance of the formation and decomposition (neglecting diffusion) of fractal elements during the evolution of the equilibrium systems as applied to the heliophysical and geomagnetic phenomena is the original position in this case. The discreteness properties of the spatial-temporal characteristics of solar activity are simply justified based on a fractal analysis. The performed calculations in the solar wind medium in the near-Earth space make it possible to classify the fluxes depending on their fractal dimension. The possible mechanism by which high-speed solar wind streams are generated is also briefly discussed in the scope of the fractal paradigm.

Performance analysis of fractal modulation transmission over fast-fading wireless channels

Fractal modulation schemes have been under investigation for signal transmission over time-varying channels because of their advantages in data transmission at different frequency bands. This also allows efficient reception when channel conditions are varying by selecting the optimal frequency/time resolution based on the current channel condition. We present a performance analysis of fractal modulation transmission over Rician fast-fading channels in the presence of AWGN. A quadrature transmission scheme is simulated and compared, in terms of error robustness, to a QAM transmission system. Other papers analysing fractal modulation system performance do not consider time-varying channels, which are important as they represent the main configuration for communication systems based on this modulation technique. The novelty of our paper lies in the comparison of a fractal modulation system to a QAM one (core of the OFDM modulation technology, extensively used in broadcasting) using a testbed simulation environment where additive noise and fast fading are considered as typical error sources for transmission over wireless channels. Several wavelet families for a fractal modulation scheme have been considered and performance for each one measured; results reported show the effectiveness of the fractal modulation paradigm and confirm its effective utilization in data broadcasting.

Self-organized complexity in the physical, biological, and social sciences.

The National Academy of Sciences convened an Arthur M. Sackler Colloquium on “Self-organized complexity in the physical, biological, and social sciences” at the NAS Beckman Center, Irvine, CA, on March 23–24, 2001. The organizers were D.L.T. (Cornell), J.B.R. (Colorado), and Hans Frauenfelder (Los Alamos National Laboratory, Los Alamos, NM). The organizers had no difficulty in finding many examples of complexity in subjects ranging from fluid turbulence to social networks. However, an acceptable definition for self-organizing complexity is much more elusive. Symptoms of systems that exhibit self-organizing complexity include fractal statistics and chaotic behavior. Some examples of such systems are completely deterministic (i.e., fluid turbulence), whereas others have a large stochastic component (i.e., exchange rates). The governing equations (if they exist) are generally nonlinear and may also have a stochastic driver. Many of the concepts that have evolved in statistical physics are applicable (i.e., renormalization group theory and self-organized criticality). As a brief introduction, we consider a few of the symptoms that are associated with self-organizing complexity. The classic example of self-organizing complexity is the frequency-size distribution of earthquakes. Earthquakes are certainly complex yet they universally satisfy the relation (to a good approximation) ![Formula][1] where N is the number of earthquakes in a specified time interval and region with their rupture area greater than A . This is the well known Guttenberg–Richter relation (1). The scaling exponent D is the fractal dimension introduced by B. Mandelbrot (2). In his book, Mandelbrot (3) pointed out the wide range of validity of the fractal scaling relation ![Formula][2] where Ni is the number of objects of size ri . Power-law scaling is second only to the Gaussian distribution in terms of applicability. Its relatively recent acceptance, in terms of the fractal paradigm, can be attributed to the fact that it cannot be used as … [1]: /embed/tex-math-1.gif [2]: /embed/tex-math-2.gif