New library of phase-change materials with their selection by the Rényi entropy method.

The secret to the successful and widespread deployment of solar energy for thermal applications is effective and affordable heat storage. The ability to provide a high energy storage density and the capacity to store heat at a constant temperature corresponding to the phase transition temperature of the heat storage material (phase-change material or PCM) make latent heat storage one of the most alluring methods of heat storage. Today, it can be challenging to obtain all the published data on PCM qualities, including relevant non-thermodynamic properties in addition to thermodynamic ones. The developed new PCM library contains various types of PCMs which possess broad range of operation temperatures. This new library consists of 500 substances along with nine associated properties such as phase change temperature, solidification temperature, maximum operation temperature, density, latent heat and specific heat capacity, thermal conductivity, cycleability and ignition temperature. Furthermore, a new PCM selection method, based on calculating the Rényi entropy for a given set of selection criteria, has been proposed. The newly developed selection method requires no subjective judgements. The idea of the method is inspired by earlier applications of fractal analysis methods in many areas of research.

A non-field analytical method for gas dissolution under forced compression.

This paper presents an extension of the non-field analytical method-known as the method of Kulish-to model gas dissolution into a liquid due to forced compression. Solutions are obtained for the time evolution of pressure (and, hence, mass concentration) at the gas-liquid interface. These solutions are in the form of series with respect to fractional differ-integral operators. The asymptotic solutions for the two limiting cases of compression-slow and fast compression-have been established as well. Then several particular examples of the law of gas volume variation are considered. Among them, the law of a linear volume variation is the most interesting for practical purposes, in which case numerical values of the dimensionless pressure as a function of dimensionless time are provided.

Information-based analysis of the coupling between brain and heart reactions to olfactory stimulation.

BACKGROUND: Analysis of the heart activity is one of the important areas of research in biomedical science and engineering. For this purpose, scientists analyze the activity of the heart in various conditions. Since the brain controls the heart's activity, a relationship should exist among their activities. OBJECTIVE: In this research, for the first time the coupling between heart and brain activities was analyzed by information-based analysis. METHODS: Considering Shannon entropy as the indicator of the information of a system, we recorded electroencephalogram (EEG) and electrocardiogram (ECG) signals of 13 participants (7 M, 6 F, 18-22 years old) in different external stimulations (using pineapple, banana, vanilla, and lemon flavors as olfactory stimuli) and evaluated how the information of EEG signals and R-R time series (as heart rate variability (HRV)) are linked. RESULTS: The results indicate that the changes in the information of the R-R time series and EEG signals are strongly correlated (ρ=-0.9566). CONCLUSION: We conclude that heart and brain activities are related.

Modelling the behaviour of thermal energy harvesting devices with phase-change materials.

This paper presents a new general theoretical model of thermal energy harvesting devices (TEHDs), which utilise phase-change materials (PCMs) for energy storage. The model's major goal is to identify a set of parameters under which these devices perform optimally, that is, attain the largest thermal buffering capacity and exchange heat with the surrounding phase as quickly as possible. For the first time, an expression for the characteristic harvesting time is developed from the constructal theory viewpoint under the optimal performance assumption, and a dimensionless criterion that characterizes PCM performance is provided. Furthermore, a new non-field solution of the energy equation governing the process of heat transfer within TEHDs with PCMs has also been derived. An expression for the effective thermal effusivity is then obtained. Finally, under a given set of boundary conditions and geometrical constraints, a novel simple technique for the optimal choice of PCMs in TEHDs has been established.

A non-field analytical method for heat transfer problems through a moving boundary.

This paper presents an extension of the non-field analytical method-known as the method of Kulish-to solving heat transfer problems in domains with a moving boundary. This is an important type of problems with various applications in different areas of science. Among these are heat transfer due to chemical reactions, ignition and explosions, combustion, and many others. The general form of the non-field solution has been obtained for the case of an arbitrarily moving boundary. After that some particular cases of the solution are considered. Among them are such cases as the boundary speed changing linearly, parabolically, exponentially, and polynomially. Whenever possible, the solutions thus obtained have been compared with known solutions. The final part of the paper is devoted to determination of the front propagation law in Stefan-type problems at large times. Asymptotic solutions have been found for several important cases of the front propagation.

A non-field analytical method for solving problems in aero-acoustics.

In 2000, a non-field analytical method for solving various problems of energy and information transport has been developed by Kulish and Lage. Based on the Laplace transform technique, this elegant method yields closed-form solutions written in the form of integral equations, which relate local values of an intensive properties such as, for instance, velocity, mass concentration, temperature with the corresponding derivative, that is, shear stress, mass flux, temperature gradient. Over the past 20 years, applied to solving numerous problems of energy and information transport, the method-now known as the method of Kulish-proved to be very efficient. In this paper-for the first time-the method is applied to problems in aeroacoustic. As a result, an integral relation between the local values of the acoustic pressure and the corresponding velocity perturbation has been derived. The said relation is valid for axisymmetric cases of planar, cylindrical and spherical geometries.

Physiological State and Learning Ability of Students in Normal and Virtual Reality Conditions: Complexity-Based Analysis.

BACKGROUND: Education and learning are the most important goals of all universities. For this purpose, lecturers use various tools to grab the attention of students and improve their learning ability. Virtual reality refers to the subjective sensory experience of being immersed in a computer-mediated world, and has recently been implemented in learning environments. OBJECTIVE: The aim of this study was to analyze the effect of a virtual reality condition on students' learning ability and physiological state. METHODS: Students were shown 6 sets of videos (3 videos in a two-dimensional condition and 3 videos in a three-dimensional condition), and their learning ability was analyzed based on a subsequent questionnaire. In addition, we analyzed the reaction of the brain and facial muscles of the students during both the two-dimensional and three-dimensional viewing conditions and used fractal theory to investigate their attention to the videos. RESULTS: The learning ability of students was increased in the three-dimensional condition compared to that in the two-dimensional condition. In addition, analysis of physiological signals showed that students paid more attention to the three-dimensional videos. CONCLUSIONS: A virtual reality condition has a greater effect on enhancing the learning ability of students. The analytical approach of this study can be further extended to evaluate other physiological signals of subjects in a virtual reality condition.

Enhanced Thermal Buffering of Phase Change Materials by the Intramicrocapsule Sub per Mille CNT Dopant.

Microencapsulation of a carbon nanotube (CNT)-loaded paraffin phase change material, PCM in a poly(melamine-formaldehyde) shell, and the respective CNT-PCM gypsum composites is explored. Although a very low level (0.001-0.1 wt %) of intramicrocapsule loading of CNT dopant does not change the thermal conductivity of the solid, it increases the measured effusivity and thermal buffering performance during phase transition. The observed effusivity of 0.05 wt % CNT-doped PCM reaches 4000 W s-0.5 m-2 K-1, which is higher than the reported effusivity of alumina and alumina bricks and an order of magnitude larger than the solid, CNT-free PCM powder. The CNT dopant (0.015 wt %) in a 30 wt % PCM-plaster composite improved the effusivity by 60% compared to the CNT-free composite, whereas the addition of the same amount of CNTs to the bulk of the plaster does not improve either the effusivity or the thermal buffering performance of the composite. The thermal enhancement is ascribed to a CNT network formation within the paraffin core.

Retraction: Fractal Based Analysis of the Influence of Odorants on Heart Activity.

This corrects the article DOI: 10.1038/srep38555.

Retraction: The Analysis of the Influence of Odorant's Complexity on Fractal Dynamics of Human Respiration.

This corrects the article DOI: 10.1038/srep26948.

Retraction: The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal.

This corrects the article DOI: 10.1038/srep26639.

Retraction: Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells.

This corrects the article DOI: 10.1038/srep13583.

The fractal based analysis of human face and DNA variations during aging.

Human DNA is the main unit that shapes human characteristics and features such as behavior. Thus, it is expected that changes in DNA (DNA mutation) influence human characteristics and features. Face is one of the human features which is unique and also dependent on his gen. In this paper, for the first time we analyze the variations of human DNA and face simultaneously. We do this job by analyzing the fractal dimension of DNA walk and face during human aging. The results of this study show the human DNA and face get more complex by aging. These complexities are mapped on fractal exponents of DNA walk and human face. The method discussed in this paper can be further developed in order to investigate the direct influence of DNA mutation on the face variations during aging, and accordingly making a model between human face fractality and the complexity of DNA walk.

Mathematical-based modeling and prediction of the effect of external stimuli on human gait.

Human gait is defined as human locomotion that is achieved through the movement of limbs. Different limb movement patterns result in different gait patterns. Different internal and external stimuli can affect the human gait. During the years, scientists have worked on the analysis of the effect of external stimuli on human gait, but no work has been reported yet that suggests a mathematical model for analysis of this effect by linking to the nervous system. Considering the diffusion of external stimuli to the nervous system on one side and fractality of human gait on another side, in this research, for the first time, we develop a model for prediction of human gait using fractional diffusion equation. Using this model, we will predict the effect of auditory stimuli on human gait. The model developed in this research is useful not only for analysis of the effect of auditory stimuli on human gait but can be used also for analysis of different types of stimuli on subjects with healthy conditions or having some types of diseases. Copyright © 2016 John Wiley & Sons, Ltd.

Fractal Based Analysis of the Influence of Odorants on Heart Activity.

An important challenge in heart research is to make the relation between the features of external stimuli and heart activity. Olfactory stimulation is an important type of stimulation that affects the heart activity, which is mapped on Electrocardiogram (ECG) signal. Yet, no one has discovered any relation between the structures of olfactory stimuli and the ECG signal. This study investigates the relation between the structures of heart rate and the olfactory stimulus (odorant). We show that the complexity of the heart rate is coupled with the molecular complexity of the odorant, where more structurally complex odorant causes less fractal heart rate. Also, odorant having higher entropy causes the heart rate having lower approximate entropy. The method discussed here can be applied and investigated in case of patients with heart diseases as the rehabilitation purpose.

Analysis of the Influence of Complexity and Entropy of Odorant on Fractal Dynamics and Entropy of EEG Signal.

An important challenge in brain research is to make out the relation between the features of olfactory stimuli and the electroencephalogram (EEG) signal. Yet, no one has discovered any relation between the structures of olfactory stimuli and the EEG signal. This study investigates the relation between the structures of EEG signal and the olfactory stimulus (odorant). We show that the complexity of the EEG signal is coupled with the molecular complexity of the odorant, where more structurally complex odorant causes less fractal EEG signal. Also, odorant having higher entropy causes the EEG signal to have lower approximate entropy. The method discussed here can be applied and investigated in case of patients with brain diseases as the rehabilitation purpose.

Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal.

One of the major challenges in brain research is to relate the structural features of the auditory stimulus to structural features of Electroencephalogram (EEG) signal. Memory content is an important feature of EEG signal and accordingly the brain. On the other hand, the memory content can also be considered in case of stimulus. Beside all works done on analysis of the effect of stimuli on human EEG and brain memory, no work discussed about the stimulus memory and also the relationship that may exist between the memory content of stimulus and the memory content of EEG signal. For this purpose we consider the Hurst exponent as the measure of memory. This study reveals the plasticity of human EEG signals in relation to the auditory stimuli. For the first time we demonstrated that the memory content of an EEG signal shifts towards the memory content of the auditory stimulus used. The results of this analysis showed that an auditory stimulus with higher memory content causes a larger increment in the memory content of an EEG signal. For the verification of this result, we benefit from approximate entropy as indicator of time series randomness. The capability, observed in this research, can be further investigated in relation to human memory.

Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors.

Cancer is a class of diseases characterized by out-of-control cells' growth which affect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. The anticancer drug travels to the tumor and then diffuses in it through capillaries. The diffusion of drugs in the solid tumor is limited by penetration depth which is different in case of different drugs and cancers. The computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many efforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, first we propose phase lagging model for diffusion of drug in the tumor. Then, using this model on one side and considering the classic diffusion on the other side, we compute the drug penetration depth in the solid tumor. This computed value of drug penetration depth is corroborated by comparison with the values measured by experiments.

The Analysis of the Influence of Odorant's Complexity on Fractal Dynamics of Human Respiration.

One of the major challenges in olfaction research is to relate the structural features of the odorants to different features of olfactory system. However, no relationship has been yet discovered between the structure of the olfactory stimulus, and the structure of respiratory signal. This study reveals the plasticity of human respiratory signal in relation to 'complex' olfactory stimulus (odorant). We demonstrated that fractal temporal structure of respiration dynamics shifts towards the properties of the odorants used. The results show for the first time that more structurally complex a monomolecular odorant will result in less fractal respiratory signal. On the other hand, odorant with higher entropy will result the respiratory signal with lower entropy. The capability observed in this research can be further investigated and applied for treatment of patients with different respiratory diseases.

The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal.

One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the 'complex' visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.