Search Results (44)

A new methodology is introduced that incorporates advanced higher moment evaluation in a new approach to the Portfolio Selection problem, supported by effective Computational Intelligence models. The Portfolio Intelligence (PI) model extracts hidden patterns from numerous accounting data and financial statements, filtering misleading effects such as noise or fraud offering an optimal portfolio selection method. The chaotic reflections of speculative behaviors of investors are analyzed in fractal distributions, as higher moments with fundamentals clear the turbulence of noise while the PI model, under its robust AI classifiers, provides optimal investment support. Full article

In this work, we present a new partially coherent adjustable anomalous vortex laser beam (PCAAVLB) and introduce it into turbulent biological tissue. The equation of such PCAAVLB in turbulent biological tissue is obtained. By numerical analysis, the evolution of the intensity of such PCAAVLB in turbulent biological tissue is analyzed. It is found that the PCAAVLB in biological tissue can lose its ring shape and become a Gaussian beam, and a PCAAVLB with smaller topological charge $M$ or coherence length $\sigma$ will evolve into a Gaussian profile faster. The PCAAVLB in turbulent biological tissue with a smaller small-length-scale factor $l_0$ or larger fractal dimension $D$ will evolve into a Gaussian profile faster and have a larger intensity as z increases. The results may have potential applications in sensing under biological tissue environments and laser imaging in biology. Full article

Methanol, a renewable and sustainable fuel, provides an effective strategy for reducing greenhouse gas emissions when synthesized through carbon dioxide hydrogenation integrated with carbon capture technology. The incorporation of hydrogen into methanol-fueled engines enhances combustion efficiency, mitigating challenges such as pronounced cycle-to-cycle variations and cold-start difficulties. A simulation framework was developed using Python 3.13 and the Cantera 3.1.0 library to model the combustion system of a four-stroke spark-ignited (SI) methanol–hydrogen engine. This framework integrates a fractal turbulent combustion model with chemical reaction kinetics, complemented by early flame development and near-wall combustion models to address limitations during the initial and terminal combustion phases. The model was validated by using experimental data measured from a spark-ignited methanol engine. The effects of varying Hydrogen Energy Rates (HER) on engine power performance, combustion characteristics, and emissions (like formaldehyde and carbon monoxide) were subsequently analyzed under different operating loads, whilst the knock limit boundaries were established for different operational conditions. Findings demonstrate that increasing HER improves the engine power output and thermal efficiency, shortens the combustion duration, and reduces the formaldehyde and carbon monoxide emissions. Nevertheless, under high-load conditions, higher HER increases the knocking tendency, which constrains the maximum permissible HER decreasing from approximately 40% at 15% load to 20% at 100% load. The model has been developed into a Python library and will be open-sourced on Github. Full article

This paper reports the improved thermal and drying performance of a solar air heater powered by real solar irradiance and equipped with a tree-like fractal-based cylindrical pin (SAH-TFCP) as a turbulator for drying applications. The main purpose of this work is to demonstrate the SAH-TFCP’s improvement potential based on its thermal and drying performance as compared with a conventional solar air heater based on a flat-plate absorber (SAH-FP). The test was implemented based on solar time from 8:30 to 17:30 under Thailand’s climatic conditions at a latitude angle of 14° and a longitude angle of 100°. Turmeric slices were used to evaluate the SAH’s drying performance. The thermal efficiency, moisture content wet basis (MC_wb), drying rate (DR), and drying efficiency were measured as parameters of interest to assess the improvement potential of the SAH-TFCP over the SAH-FP. The results indicate that the SAH-TFCP provides better thermal and drying performance than the SAH-FP. A higher flow rate yields a higher thermal efficiency and a greater improvement potential. The improvement potential is around 44–85%. The drying efficiency of the SAH-TFCP is always higher than that of the SAH-FP and has an improvement potential of 32–44%, depending on the airflow rate. Full article

To achieve low-cost and on-demand launches of microsatellites, the authors have been researching and developing a micro hybrid rocket since 2014. In 2018, a ballistic launch experiment was performed using the developed hybrid rocket, where it reached an altitude of about 6.2 km. The rocket engine had a 3D-printed solid fuel grain made of acrylonitrile butadiene styrene (ABS) resin in combination with a nitrous oxide oxidizer. The fuel grain port had a star-fractal swirl geometry in order to increase the surface area of the port, to promote the laminar–turbulent transition by increasing the friction resistance, and to give a swirling velocity component to the oxidizer flow. This overcame the hybrid rocket’s drawback of a low fuel regression rate; i.e., it achieved a higher fuel gas generation rate compared with a classical port geometry. In 2021, the hybrid rocket engine was scaled up, and its total impulse was increased to over 50 kNs; it reached an altitude of 15 km. In addition to the engine, other components were also improved, such as through the incorporation of lightweight structures, low-shock separation devices, a high-reliability telemetry device, and a data logger, while keeping costs low. The rocket was launched and reached an altitude of about 10.1 km, which broke the previous Japanese altitude record of 8.3 km for hybrid rockets. This presentation will report on the developed components from the viewpoint of system design and the results of the ballistic launch experiments. Full article

The Rank-Ordered Multifractal Analysis (ROMA) is a tool designed to characterize scale (in)variance and multifractality based on rank ordering the fluctuations in “groups” characterized by the same mono-fractal behavior (Hurst exponent). A range-limited structure-function analysis provides the mono-fractal index for each rank-ordered range of fluctuations. We discuss here two examples of multi-scale solar wind turbulence and complexity where ROMA is applied on the following: (a) data collected by Ulysses spacecraft in the fast solar wind, outside the ecliptic, between 25 and 31 January 2007, at roughly 2.5 Astronomical Units (AU) from the Sun, in the Southern heliosphere, at latitudes between −76.5 and −77.3 degrees, and (b) slow solar wind data collected in the ecliptic plane by Venus Express spacecraft, at 0.72 AU, on 28 January 2007. The ROMA spectrum of fast solar wind derived from ULYSSES data shows a scale-dependent structure of fluctuations: (1) at the smallest/kinetic range of scales (800 to 3200 km), persistent fluctuations are dominant, and (2) at the inertial range of scales (10⁴ to 2 × 10⁵ km), anti-persistent fluctuations are dominant, but less clearly developed and possibly indicative for the development of instabilities with cross-over behavior. The ROMA spectrum of the slow solar wind derived from Venus Express data, suggests a different structure of turbulence: (1) fully developed multifractal turbulence across scales between 5 × 10⁴ and 4 × 10⁵ km, with the Hurst index changing from anti-persistent to persistent values for the larger amplitude magnetic fluctuations; (2) at the smallest scales (400 to 6400 km), fluctuations are mainly anti-persistent, and the ROMA spectrum indicates a tendency towards mono-fractal behavior. Full article

After hydraulic fracturing, unconventional reservoirs frequently encounter challenges related to limited effective proppant support distance and suboptimal proppant placement. Due to the strong heterogeneity of offshore reservoirs, which causes varying fracture roughnesses depending on different lithologies, a systematic study of the relationship between roughness and proppant transport could optimize operational parameters. This study incorporates the box dimension method for fractal dimension analysis to quantify roughness in auto-correlated Gaussian distributed surfaces created by true triaxial tests. Combined with the numerical analysis of (computational fluid dynamics) CFD-DEM (discrete element method) for bidirectional coupling, the laws of proppant deposition and transport processes within fractures with different roughnesses are obtained through comparative verification simulations. The results show that for rougher fractures of shale, the proppants are transported farther, but at JRC_52, (joint roughness coefficient), where there may be plugging in curved areas, there is a risk of near-well blockages. Compared to the smooth model, fluctuations in JRC_28 (tight sandstone) drastically increase turbulent kinetic energy within the fracture, altering particle transport dynamics. Moreover, smaller proppants (d/w ≤ 0.3) exhibit better transport capacity due to gravity, but the conductivity of the proppant is limited when the particles are too small. A d/w of 0.4 is recommended to guarantee transport capacity and proppant efficiency near the well. Additionally, proppants injected sequentially from small to large in shale fractures offer optimal propping effects, and can take advantage of the better transport capacity of smaller proppants in rough fractures. The large proppant (d/w = 0.8) is primarily deposited by gravity and forms a sloping sand bed, which subsequently ensures the aperture of the fractures. This research provides a fresh perspective on the influence of fracture roughness on proppant transport in offshore unconventional reservoirs and offers valuable considerations for the order of proppant injection. Full article

Atmospheric turbulence, recognized as a quintessential space–time chaotic system, can be characterized by its fractal properties. The characteristics of the time series of multiple orders of fractal dimensions, together with their relationships with stability parameters, are examined using the data from an observational station in Horqin Sandy Land to explore how the diurnal variation, synoptic process, and stratification conditions can affect the fractal characteristics. The findings reveal that different stratification conditions can disrupt the quasi-three-dimensional state of atmospheric turbulence in different manners within different scales of motion. Two aspects of practical applications of fractal dimensions are explored. Firstly, fractal properties can be employed to refine similarity relationships, thereby offering prospects for revealing more information and expanding the scope of application of similarity theories. Secondly, utilizing different orders of fractal dimensions, a systematic algorithm is developed. This algorithm distinguishes and eliminates non-turbulent motions from observational data, which are shown to exhibit slow-changing features and result in a universal overestimation of turbulent fluxes. This overestimation correlates positively with the boundary frequency between turbulent and non-turbulent motions. The evaluation of these two aspects of applications confirms that fractal properties hold promise for practical studies on atmospheric turbulence. Full article

This article begins with an interdisciplinary review of a hydrodynamic approach to understanding the origins and nature of macroscopic quantum phenomena in high-temperature superconductivity, superfluidity, turbulence and biological systems. Building on this review, we consider new theoretical insights into the origin and nature of pointer states and their role in the emergence of quantum systems. The approach includes a theory of quantum coherence underpinned by turbulence, generated by a field of pointer states, which take the form of recirculating, spin-1/2 vortices (toroids), interconnected via a cascade of spin-1 vortices. Decoherence occurs when the bosonic network connecting pointer states is disrupted, leading to their localisation. Building further on this work, we explore how quantum particles (in the form of different vortex structures) could emerge as the product of a causal dynamic process, within a turbulent (fractal) spacetime. The resulting particle structures offer new insights into intrinsic spin, the probabilistic nature of the wave function and how we might consider pointer states within the standard “point source” representation of a quantum particle, which intuitively requires a more complexed description. Full article

We present a new perspective on the symmetries that govern the formation of large-scale structures across the Universe, particularly focusing on the transition from the seeds of galaxy clusters to the seeds of galaxies themselves. We address two main features of cosmological fluid dynamics pertaining to both the linear and non-linear regimes. The linear dynamics of cosmological perturbations within the Hubble horizon is characterized by the Jeans length, which separates stable configurations from unstable fluctuations due to the gravitational effect on sufficiently large (and therefore, massive enough) overdensities. On the other hand, the non-linear dynamics of the cosmological fluid is associated with a turbulent behavior once the Reynolds numbers reach a sufficiently high level. This turbulent regime leads to energy dissipation across smaller and smaller scales, resulting in a fractal distribution of eddies throughout physical space. The proposed scenario suggests that the spatial scale of eddy formation is associated with the Jeans length of various levels of fragmentation from an original large-scale structure. By focusing on the fragmentation of galaxy cluster seeds versus galaxy seeds, we arrived at a phenomenological law that links the ratio of the two structure densities to the number of galaxies in each cluster and to the Hausdorff number of the Universe matter distribution. Finally, we introduced a primordial magnetic field and studied its influence on the Jeans length dynamics. The resulting anisotropic behavior of the density contrast led us to infer that the main features of the turbulence could be reduced to a 2D Euler equation. Numerical simulations showed that the two lowest wavenumbers contained the major energy contribution of the spectrum. Full article

Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical principles. However, a proposed interpretation could shed light on the inherent principle behind the creation of fractals. This is the multiscale thermodynamic perspective, which states that an increase in external energy could initiate energy transport mechanisms that facilitate the dissipation or release of excess energy at different scales. Within this framework, it is revealed that power law patterns, and to a lesser extent, fractals, can emerge as a geometric manifestation to dissipate energy in response to external forces. In this context, the exponent of these power law patterns (thermodynamic fractal dimension $D$) serves as an indicator of the balance between entropy production at small and large scales. Thus, when a system is more efficient at releasing excess energy at the microscopic (macroscopic) level, $D$ tends to increase (decrease). While this principle, known as Principium luxuriæ, may sound promising for describing both multiscale and complex systems, there is still uncertainty about its true applicability. Thus, this work explores different physical, astrophysical, sociological, and biological systems to attempt to describe and interpret them through the lens of the Principium luxuriæ. The analyzed physical systems correspond to emergent behaviors, chaos theory, and turbulence. To a lesser extent, the cosmic evolution of the universe and geomorphology are examined. Biological systems such as the geometry of human organs, aging, human brain development and cognition, moral evolution, Natural Selection, and biological death are also analyzed. It is found that these systems can be reinterpreted and described through the thermodynamic fractal dimension. Therefore, it is proposed that the physical principle that could be behind the creation of fractals is the Principium luxuriæ, which can be defined as “Systems that interact with each other can trigger responses at multiple scales as a manner to dissipate the excess energy that comes from this interaction”. That is why this framework has the potential to uncover new discoveries in various fields. For example, it is suggested that the reduction in $D$ in the universe could generate emergent behavior and the proliferation of complexity in numerous fields or the reinterpretation of Natural Selection. Full article

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d>2$. This solution family is equivalent to a fractal curve in complex space ${\mathbb{C}}^d$ with random steps parametrized by N Ising variables ${\sigma }_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number r, related by $\sum {\sigma }_i=qr$. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in ${\mathbb{R}}_d$ space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size $N\to \infty$ or its chemical potential $\mu \to 0$. The system with fixed N has different asymptotics at odd and even $N\to \infty$, but the limit $\mu \to 0$ is well defined. The energy dissipation rate is analytically calculated as a function of $\mu$ using methods of number theory. It grows as $\nu /{\mu }^2$ in the continuum limit $\mu \to 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu }\to 0$. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda }$, with a continuous spectrum of indexes $\lambda$ in the local limit $\mu \to 0$. The spectrum is determined by a resolvent, which is represented as an infinite product of $3\otimes 3$ matrices depending of the element of the Euler ensemble. Full article

This paper presents a novel unsupervised deep learning methodology for the analysis of self-assembled structures formed in evaporating droplets. The proposed approach focuses on clustering these structures based on their texture similarity to characterize three different mixing procedures (turbulent, laminar, and diffusion-based) applied to produce Viscum album Quercus ${10}^{-3}$ according to the European Pharmacopoeia guidelines for the production of homeopathic remedies. Texture clustering departs from obtaining a comprehensive texture representation of the full texture patch database using a convolutional neural network. This representation is then dimensionally reduced to facilitate clustering through advanced machine learning techniques. Following this methodology, 13 clusters were found and their degree of fractality determined by means of Local Connected Fractal Dimension histograms, which allowed for characterization of the different production modalities. As a consequence, each image was represented as a vector in ${\mathbb{R}}^{13}$, enabling classification of mixing procedures via support vectors. As a main result, our study highlights the clear differences between turbulent and laminar mixing procedures based on their fractal characteristics, while also revealing the nuanced nature of the diffusion process, which incorporates aspects from both mixing types. Furthermore, our unsupervised clustering approach offers a scalable and automated solution for analyzing the databases of evaporated droplets. Full article

Insulating cotton was used to change the airflow temperature in the exhaust pipe of a diesel engine, and soot particles at different positions in the exhaust pipe under different operating conditions were collected. The morphologies and microstructures of soot particles were observed by high-resolution transmission electron microscopy (HRTEM). The characteristic parameters, including the mean primary particle diameter (d_p), radius of gyration of soot aggregate (R_g), fractal dimension of soot particle (D_f), carbon layer spacing (D_s), and carbon layer torsion resistance (T_f), were statistically analyzed. The changes in each characteristic parameter before and after adding insulating cotton were compared. After installing the cotton, soot particles still grew through surface chemical reactions and physical processes in the diesel exhaust pipe, the agglomeration becomes more and more prevalent, the particle size increased, and D_f increased. The increase in the airflow temperature in the exhaust pipe promoted the surface growth of primary soot particles and enhanced the turbulence, which made the chain-like soot particles more likely to reunite under the action of turbulent eddies. Consequently, R_g decreased and D_f increased. Furthermore, the average D_s and T_f of primary soot particles deceased, especially under high loads. This indicated that the increase in the temperature of the exhaust pipe was conducive to the graphitization of primary soot particles. Full article

A Karman vortex is a phenomenon of fluid flow that can cause fluctuation and vibration. As a result, it leads to fatigue damage to structures and induces safety accidents. Therefore, the analysis of the shedding law and strength of the Karman vortex is significant. To further understand the laws of turbulent Karman vortex shedding and strength, this study conducts a numerical vorticity simulation of a Karman vortex at the trailing edge of a hydrofoil based on the two-dimensional simplified model of the NACA0009 hydrofoil under different Reynolds numbers. Combined with image segmentation technology, the fractal characteristics of a turbulent Karman vortex at the trailing edge of a hydrofoil are extracted, the number and total area of vortex cores are calculated, and the fractal dimension of the vortex is obtained. The results show that the fractal dimension can characterize the change in vortex shape and strength under different Reynolds numbers, and that the fractal analysis method is feasible and effective for the shedding analysis of a turbulent Karman vortex. Full article