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

2020 ◽  
Vol 57 (1) ◽  
pp. 167-174
Author(s):  
Constantin Placinta ◽  
Tudor Cristian Petrescu ◽  
Vlad Ghizdovat ◽  
Stefan Andrei Irimiciuc ◽  
Decebal Vasincu ◽  
...  
Keyword(s):  
Large Class ◽  
Present Model ◽  
Period Doubling ◽  
Invariant Function ◽  
Polymer Dynamics ◽  
Advanced Materials ◽  
Structural Units ◽  
Damped Oscillations ◽  
Group Invariance ◽  
Joint Invariant

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.

scholarly journals Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1356
Author(s):  
Stefan-Andrei Irimiciuc ◽  
Alexandra Saviuc ◽  
Florin Tudose-Sandu-Ville ◽  
Stefan Toma ◽  
Florin Nedeff ◽  
...  
Keyword(s):  
Period Doubling ◽  
Nonlinear Behavior ◽  
Structural Units ◽  
Plasma Dynamics ◽  
Oscillatory Dynamics ◽  
Damped Oscillations ◽  
Hidden Symmetry ◽  
Non Linear ◽  
Transient Plasma ◽  
Newtonian Behavior

In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets.

scholarly journals Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 226
Author(s):  
Maricel Agop ◽  
Mitică Craus
Keyword(s):  
Complex System ◽  
Fractal Theory ◽  
Invariant Function ◽  
Hydrodynamic Type ◽  
Simultaneous Action ◽  
Systems Dynamics ◽  
Invariant Functions ◽  
Scale Relativity ◽  
The One ◽  
Joint Invariant

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved.

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

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2273
Author(s):  
Alexandra Saviuc ◽  
Manuela Gîrțu ◽  
Liliana Topliceanu ◽  
Tudor-Cristian Petrescu ◽  
Maricel Agop
Keyword(s):  
Fluid Dynamics ◽  
Differential Geometry ◽  
Harmonic Mapping ◽  
Period Doubling ◽  
Velocity Fields ◽  
Hydrodynamic Type ◽  
Airy Functions ◽  
Structural Units ◽  
Type Group ◽  
Complex Fluid

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.

Convolution with Odd Kernels Having a Tempered Singularity

1988 ◽  
Vol 31 (1) ◽  
pp. 3-12
Author(s):  
R. A. Kerman
Keyword(s):  
Integral Operator ◽  
Large Class ◽  
Function Space ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Invariant Function ◽  
Rearrangement Inequality

AbstractSuppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), byThen, for a large class of b one has the rearrangement inequalityThis inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.

Biomimetic materials: An introduction

1992 ◽  
Vol 50 (2) ◽  
pp. 1020-1021 ◽  
Author(s):  
M. Sarikaya ◽  
J. T. Staley ◽  
I. A. Aksay
Keyword(s):  
Self Assembly ◽  
Structural Control ◽  
Hierarchical Structures ◽  
Ceramic Composites ◽  
Advanced Materials ◽  
Length Scale ◽  
Spider Webs ◽  
Biomimetic Materials ◽  
Synthetic Materials ◽  
All Ceramic

Biomimetics is an area of research in which the analysis of structures and functions of natural materials provide a source of inspiration for design and processing concepts for novel synthetic materials. Through biomimetics, it may be possible to establish structural control on a continuous length scale, resulting in superior structures able to withstand the requirements placed upon advanced materials. It is well recognized that biological systems efficiently produce complex and hierarchical structures on the molecular, micrometer, and macro scales with unique properties, and with greater structural control than is possible with synthetic materials. The dynamism of these systems allows the collection and transport of constituents; the nucleation, configuration, and growth of new structures by self-assembly; and the repair and replacement of old and damaged components. These materials include all-organic components such as spider webs and insect cuticles (Fig. 1); inorganic-organic composites, such as seashells (Fig. 2) and bones; all-ceramic composites, such as sea urchin teeth, spines, and other skeletal units (Fig. 3); and inorganic ultrafine magnetic and semiconducting particles produced by bacteria and algae, respectively (Fig. 4).

Prospective Memory Development Across the Lifespan

2020 ◽  
Vol 25 (3) ◽  
pp. 162-173 ◽  
Author(s):  
Sascha Zuber ◽  
Matthias Kliegel
Keyword(s):  
Prospective Memory ◽  
Healthy Aging ◽  
Present Model ◽  
Current Knowledge ◽  
Well Being ◽  
The Elderly ◽  
Cognitive Factors ◽  
Everyday Functioning ◽  
Integrative Framework

Abstract. Prospective Memory (PM; i.e., the ability to remember to perform planned tasks) represents a key proxy of healthy aging, as it relates to older adults’ everyday functioning, autonomy, and personal well-being. The current review illustrates how PM performance develops across the lifespan and how multiple cognitive and non-cognitive factors influence this trajectory. Further, a new, integrative framework is presented, detailing how those processes interplay in retrieving and executing delayed intentions. Specifically, while most previous models have focused on memory processes, the present model focuses on the role of executive functioning in PM and its development across the lifespan. Finally, a practical outlook is presented, suggesting how the current knowledge can be applied in geriatrics and geropsychology to promote healthy aging by maintaining prospective abilities in the elderly.

Histological Study of Human Thyroid Gland Relative Proportion of Parenchyma and Stroma in Thyroid Glands of Bangladeshi People

2013 ◽  
Vol 1 (2) ◽  
pp. 17-20
Author(s):  
Md Enayet Ullah ◽  
Hasna Hena ◽  
Rubina Qasim
Keyword(s):  
Thyroid Gland ◽  
Histological Study ◽  
Relative Proportion ◽  
Age Groups ◽  
Human Thyroid ◽  
Structural Units ◽  
Thyroid Glands ◽  
Group A ◽  
Group B ◽  
Connective Tissue Sheath

Deep cervical fascia forms a connective tissue sheath around the thyroid gland. Delicate trabeculae and septa penetrate the gland indistinctly dividing the gland into lobes and lobules which in turn composed of follicles.1,2,3 These follicles are structural units of thyroid gland which varies greatly in size and shape.4 The number of follicles varies in different age groups. The study was carried out to see the percentage of area occupied by follicles in the stained section of thyroid glands in different age groups. The collected samples were grouped as A (3.5 – 20yrs), B (21- 40yrs) & C (41 – 78yrs). Percentage of area occupied by follicles was (58.55±10.72) in group A, (63.79±12.35) in group B + (63.39±8.29) in group C.DOI: http://dx.doi.org/10.3329/updcj.v1i2.13981 Update Dent. Coll. j. 2011: 1(2): 17-20

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