Search results for: population balance equation

Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Mehmet Yildiz, Mehmet Kale

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The primary aim of the present study was to identify the bilateral balance asymmetries when comparing the dominant (DL) vs. the non-dominant leg (NDL) in the collegian soccer players. The secondary aim was to compare the inter-limb asymmetry index (ASI) when differentiating by kicking preference (right-dominant vs. left-dominant). 34 right-dominant leg (RightDL) (age:21.12±1.85, height:174.50±5.18, weight:69.42±6.86) and 23 left-dominant leg (LeftDL), (age:21.70±2.03, height:176.2±6.27, weight:68.73±5.96) collegian football players were tested for bilateral static and dynamic balance. Balance ability was assessed by measuring centre of pressure deviation on a single leg. Single leg static and dynamic balance scores and inter-limb asymmetry index (ASI) were determined. Student t tests were used for the comparison of dominant and nondominant leg balance scores and RightDL and LeftDL football players’ inter-limb asymmetry index of the balance scores. The results showed that there were significant differences in the dynamic balance scores in favour of the nondominant leg, (DL:738±211 vs. NDL:606±226, p < 0.01). Also, it has been seen that LeftDL players have significantly higher inter-limb asymmetry index when compared with rightDL players for both static (rightDL:-7.07±94.91 vs. leftDL:-183.19±354.05, p < 0.01) and dynamic (rightDL: 1.73±49.65 vs. leftDL:27.08±23.34, p < 0.05) balance scores. In conclusion, bilateral dynamic balance asymmetries may be affected using single leg predominantly in the mobilization workouts. Because of having higher inter-limb asymmetry index, left-dominant leg players may be screened and trained to minimize balance asymmetry.

Keywords: bilateral balance, asymmetries, dominant leg, leg preference

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: S. Mousavian, A. Abedianpour, A. Khanmohammadi, S. Hematian, Gh. Eidi Veisi

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Distillation is one of the most important and utilized separation methods in the industrial practice. There are different ways to design of distillation column. One of these ways is short cut method. In short cut method, material balance and equilibrium are employed to calculate number of tray in distillation column. There are different methods that are classified in short cut method. One of these methods is Fenske-Underwood-Gilliland method. In this method, minimum reflux ratio should be calculated by underwood equation. Underwood proposed an equation that is useful for simple distillation column with one feed and one top and bottom product. In this study, underwood method is developed to predict minimum reflux ratio for column with one side stream upper than feed. The result of this model compared with McCabe-Thiele method. The result shows that proposed method able to calculate minimum reflux ratio with very small error.

Keywords: minimum reflux ratio, side stream, distillation, Underwood’s method

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Elena Listo Ubeda, Miguel Marchamalo Sacristan

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The demand for water doubles every twenty years, at a rate which is twice as fast as the world´s population growth. Despite it´s great importance, water is one of the most degraded natural resources in the world, mainly because of the reduction of natural vegetation coverage, population growth, contamination and changes in the soil use which reduces its capacity to collect water. This situation is especially serious in Central America, as reflected in the Human Development reports. The objective of this project is to assist in the improvement of water production and quality in Central America. In order to do these two watersheds in Costa Rica were selected as experiments: that of the Virilla-Durazno River, located in the extreme north east of the central valley which has an Atlantic influence; and that of the Jabillo River, which flows directly into the Pacific. The Virilla river watershed is located over andisols, and that of the Jabillo River is over alfisols, and both are of great importance for water supply to the Greater Metropolitan Area and the future tourist resorts respectively, as well as for the production of agriculture, livestock and hydroelectricity. The hydrological reaction in different soil-cover complexes, varying from the secondary forest to natural vegetation and degraded pasture, was analyzed according to the evaluation of the properties of the soil, infiltration, soil compaction, as well as the effects of the soil cover complex on erosion, calculated by the C factor of the Revised Universal Soil Loss Equation (RUSLE). A water balance was defined for each watershed, in which the volume of water that enters and leaves were estimated, as well as the evapotranspiration, runoff, and infiltration. Two future scenarios, representing the implementation of reforestation and deforestation plans, were proposed, and were analyzed for the effects of the soil cover complex on the water balance in each case. The results obtained show an increase of the ground water recharge in the humid forest areas, and an extension of the study of the dry areas is proposed since the ground water recharge here is diminishing. These results are of great significance for the planning, design of Payment Schemes for Environmental Services and the improvement of the existing water supply systems. In Central America spatial planning is a priority, as are the watersheds, in order to assess the water resource socially and economically, and securing its availability for the future.

Keywords: Costa Rica, infiltration, soil, water

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Authors: Ibrahim M. I. Hamoda, Ahmed R. Z. Baghdadi, Mohammed K. Mohamed, Nawal A. Abu-Shady

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Background: Most of patients with vestibular dysfunction suffering from balance disorders, Abnormality in balance increase effort and exertion which affect the independency, so this study might be a guide in managing balance problem and consequently improve walking with less exertion and maximum function. Purpose: to analyze and discuss the effect of transcranial magnetic therapy on balance in patients with vestibular dysfunction. Methods: forty subjects from both sexes were classified to divided randomly into two equal groups; Group I study group: this group received transcranial magnetic therapy, with a selected physical therapy program for improving balance and vestibular disorders (Balance training, Cawthorne-Cooksey Exercises) and group II (control group): this group received a selected physical therapy program as group I without transcranial magnetic therapy. This treatment procedure will be applied three times weekly for three months. The mean age was 54.53±3.44 and 55.33±2.32 years and BMI 35.7±3.03 and 35.73±1.03 kg/m2 for group I and II respectively. The Biodex Balance System, Berge balances scale (BBS) and brain MRI were used for assessment. Assessments were conducted before and after treatment. The treatment program for group I included balance training, Cawthorne-Cooksey Exercises and pulsed magnetic therapy (Parameters used in the program of 20 minutes, Intensity 2 gausses, Frequency 1 Hz). This selected program was done in approximately one hour every other day for three month. The treatment program group II Patients received the same program as group A without transcranial magnetic therapy. Results: The One-way ANOVA revealed that there were no significant differences in BBS scores, overall balance index, Anterior / posterior balance index, Medial / lateral balance index and dynamic limits of stability between both groups. Moreover, the BBS scores increased and overall balance index, Anterior / posterior balance index, Medial / lateral balance index and dynamic limits of stability decreased significantly after treatment in group I and II compared with before treatment. Interpretation/Conclusion: Adding pulsed magnetic therapy to balance training, Cawthorne-Cooksey Exercises has no effect on static and dynamic balance in patients with balance problems due to benign positional paroxysmal vertigo.

Keywords: balance, transcranial magnetic therapy, vestibular dysfunction, biomechanic

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Authors: Dhruveshi B. Rana, Nirav P. Vaghela, Jigar N. Mehta

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Objective: To assess the relationships among age, gender, anthropometrics and dynamic balance in 5 to 12 years of children in Anand city. Method: Cross-sectional study was conducted. 150 school going children of 5-12 (75-girls, 75-boys) years were recruited from the school of the Anand city-Shivam English Medium school, Veer Vithalbhai Patel school, Adarsh Primary school. Height, weight, arm length, and foot length were measured in 150 children of 5 to 12 years. Dynamic balance was assessed using Time Up and Go Test, Functional Reach Test, Pediatric Balance Scale. Results: Positive relationship (r = 0.58 and r= 0.77) were found between increasing age and FRT and PBS scores. A negative relationship (r = - 0.46) was observed between age of boys and TUG test. Significant gender by age group difference was observed in FRT. Arm length and height has the strongest influence on FRT, and age, height, foot length; and arm length has the strongest influence on PBS. Conclusions: Age and arm length have the strongest relationship with the dynamic balance (FRT, PBS). Dynamic balance ability is directly related to the age. It helps the pediatric therapists in selecting dynamic balance test according to the age.

Keywords: age, gender, anthropometric, dynamic balance

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Authors: Hatice Torcu Koc, Zeliha Erdogan

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This study presented the investigation of the population structure of Upeneus moluccensis in order to provide further knowledge and to compare the data with the studies before and thus help in the management of the population in the İskenderun Bay. For this purpose, a total of 370 golden-banded goatfish were caught by a commercial vessel monthly at a depth of 50-60 m. from İskenderun Bay in the years 2016-2018. Von Bertalanffy growth equation,length-weight relationships, sex ratio, age, condition, and gonado and hepato-somatic index values of U.peneus moluccensis specimens were determined. For this, the lengths and weights were measured using a dial caliper of 0.05 mm and a sensitive balance. Total lengths were 7.2–17.5 cm in females and 7.0–17.9 cm in males, while total weight ranges for females and males were 3.91-64.26 g and 3.69-60.95 g., respectively. Length-weight relationship for all individuals was calculated as W=0.004*L³ ³⁸, R²=0.85. Growth parameter was determined as L∞= 20.75 cm, k=0.33, t₀= - 0.56. The age readings were done by using the Bhattacharya method. The population was composed of 3 ages (1-3). The sex ratio was found as 1:1.42, corresponding to 41.4% males and 58.6% females, in favor of females (p<0.05). Values of the average condition and hepatosomatic index were found to be shown a similar pattern for males (1.088, 1.104) and females (1.124, 1.177), respectively. According to GSI values, the spawning period started in March and increased to April, May, and September. It was estimated that total (Z) mortality, natural (M) mortality, and fishing (F) mortality rates were estimated as Z=0.94 year-¹, M=0.033 year-¹, and F=0.63 year-¹, respectively. As the exploitation rate was estimated to be E=0.67, it can be shown that the golden-banded goatfish stock was influenced by overfishing. The findings of this study are very important to point out the population of U. moluccensis, which penetrated into the eastern Mediterranean Sea of Türkiye due to global heating and the construction of the Suez Canal and to be basic data for the next fisheries investigations.

Keywords: biology, U. moluccensis, invasive, lessepsian, İskenderun Bay

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: Syeda Faiza Gardazi, Syed Ahsan Ali Gardazi, Ajmal Waheed

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The trend of overtime is increasing among workers due to more pressure to perform workloads, job insecurity, and financial issues. Overtime work affects the work-life balance conflict negatively as well positively. Work-life balance conflict has become an important issue as traditional work and family roles have changed. The purpose of the current research was to study the impact of overtime work on work-life balance conflict along with the moderating role of job satisfaction. For this purpose, data is collected from the employees working in different public and private sectors of Pakistan using simple random sampling technique. Descriptive statistics was used for data presentation and analysis. Correlation and regression analysis were used to test four research hypotheses proposed on the basis of research framework. The findings led to the acceptance of four hypotheses. The results show that high working hours and overtime in general lead to high work-life balance conflict. Moreover, job satisfaction moderates the relationship between overtime work and work-life balance conflict.

Keywords: family to work conflict, overtime work, work to family conflict, work-life balance conflict

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Authors: Hakan Erol, Altan Elibol, Ömer Eryılmaz, Mehmet Şimşek

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Organizations aim to manage information in a most possible effective way for sustainment and development. In doing so, they apply various procedures and methods. The very same situation is valid for each service of Armed Forces. During long-lasting endeavors such as shaping and maintaining security environment, supporting and securing peace, knowledge management is a crucial asset. Optimum Balance Model aims to promote the system from a decisive point to a higher decisive point. In this context, this paper analyses the application of optimum balance model to knowledge management in Armed Forces and tries to find answer to the question how Optimum Balance Model is integrated in knowledge management.

Keywords: optimum balance model, knowledge management, security environment, supporting peace

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Authors: Wai Sang Wu, Florence Pik Sze Mok

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Introduction: Ageing population is one of the hot topics nowadays in the world and this phenomenon is believed to exacerbate continuously in the future. According to the latest information from World Health Organization (WHO) in 2016, the proportion of people aged more than 60 years is projected to be doubled from 12% in 2015 to 22% in 2050 of the world's population. Similarly, according to figures released by the Census and Statistic Department of Hong Kong in 2015, the contribution of elderly aged more than 65 years olds is projected to increase from 15% in 2014 to 34% in 2064 in local community. On the other hand, falls in elderly is a common problem, and it can bring along many negative consequences among elders, such as reducing their mobility level as well as their quality of life. In addition, it can also increase the caring stress of their family caregivers and as well increase the reliance and burden on the medical care system of Hong Kong. Therefore, appropriate measures should be implemented in order to minimize the risk of fall among elders. The objective of this study is to evaluate the effectiveness of the chair-based exercise programme in affecting the balance of the elderly in Hong Kong. Methods: Thirteen healthy subjects (males = 2; females = 11; mean age: 76.2 ± 7.8 years old) were recruited from an elderly social centre in the community to participate in a structural chair-based exercise programme for 6 weeks (1 session per week; 60-minutes per session). Subjects were being assessed on their balance ability using three commonly used clinical assessments, namely, 1) single leg stance (SLS) test, 2) functional reach test, and 3) 360-degree turn test, before and after their participation in the chair-based exercise programme. Pre and post within-subject comparison was adopted to assess the effectiveness of the programme. Results: There was significant improvement (p < 0.05) in all balance parameters of the subjects after their participation in the exercise programme. Elderly demonstrated significant improvement in SLS (p < 0.012), functional reach (p < 0.030) and 360 degree turn (p < 0.043). Conclusions: This study showed that a community chair-based exercise programme is effective in improving the balance ability of the elders. It seems to be another exercise regime that should be promoted among the elders in order to minimize their risk of falls and its negative consequence.

Keywords: balance, chair-based exercise programme, community, elderly

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Authors: A. Fogliata, L. Martiniello, A. Ambretti

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Introduction: The significance of balance and stability in physical education among adolescents is well-established. This study aims to assess the efficacy of Centering (CENT), which employs intra-abdominal pressure (IAP) in line with the Synchrony Method, in optimizing balance and reducing perceived stress. Materials and Methods: A 6-week intervention was conducted on a sample of adolescents, divided into a control group and an experimental group that incorporated CENT into their physical education program. The Stork Balance Test and the Perceived Stress Scale (PSS) were used to measure changes. Results: Findings revealed a significant enhancement in the balance of both the dominant and non-dominant limbs in the experimental group compared to the control group. Moreover, the PSS test indicated a reduction in perceived stress within the experimental group. Conclusion: Integrating the centering technique into physical education programs can lead to substantial improvements in adolescents' balance and stability, in addition to a reduction in perceived stress levels. These findings suggest the need for further research on broader populations to solidify these pivotal outcomes.

Keywords: adolescents, physical education, balance, centering, intra-abdominal pressure

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Authors: Yanto Santosa, Dede Aulia Rahman, Cory Wulan, Abdul Haris Mustari

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The global demand for long-tailed macaques for medical experimentation has continued to increase. Fulfillment of Indonesian export demands has been mostly from natural habitats, based on a harvesting quota. This quota has been determined according to the total catch for a given year, and not based on consideration of any demographic parameters or physical environmental factors with regard to the animal; hence threatening the sustainability of the various populations. It is therefore necessary to formulate a method for calculating a sustainable harvesting quota, based on population parameters in natural habitats. Considering the possibility of variations in habitat characteristics and population parameters, a time series observation of demographic and physical/biotic parameters, in various habitats, was performed on 13 groups of long-tailed macaques, distributed throughout the West Java, Lampung and Yogyakarta areas of Indonesia. These provinces were selected for comparison of the influence of human/tourism activities. Data on population parameters that was collected included data on life expectancy according to age class, numbers of individuals by sex and age class, and ‘ratio of infants to reproductive females’. The estimation of population growth was based on a population dynamic growth model: the Leslie matrix. The harvesting quota was calculated as being the difference between the actual population size and the MVP (minimum viable population) for each sex and age class. Observation indicated that there were variations within group size (24 – 106 individuals), gender (sex) ratio (1:1 to 1:1.3), life expectancy value (0.30 to 0.93), and ‘ratio of infants to reproductive females’ (0.23 to 1.56). Results of subsequent calculations showed that sustainable harvesting quotas for each studied group of long-tailed macaques, ranged from 29 to 110 individuals. An estimation model of the MVP for each age class was formulated as Log Y = 0.315 + 0.884 Log Ni (number of individual on ith age class). This study also found that life expectancy for the juvenile age class was affected by the humidity under tree stands, and dietary plants’ density at sapling, pole and tree stages (equation: Y= 2.296 – 1.535 RH + 0.002 Kpcg – 0.002 Ktg – 0.001 Kphn, R2 = 89.6% with a significance value of 0.001). By contrast, for the sub-adult-adult age class, life expectancy was significantly affected by slope (equation: Y=0.377 = 0.012 Kml, R2 = 50.4%, with significance level of 0.007). The infant to reproductive female ratio was affected by humidity under tree stands, and dietary plant density at sapling and pole stages (equation: Y = -1.432 + 2.172 RH – 0.004 Kpcg + 0.003 Ktg, R2 = 82.0% with significance level of 0.001). This research confirmed the importance of population parameters in determining the minimum viable population, and that MVP varied according to habitat characteristics (especially food availability). It would be difficult therefore, to formulate a general mathematical equation model for determining a harvesting quota for the species as a whole.

Keywords: harvesting, long-tailed macaque, population, quota

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Andreia Guimaraes Farnese, Mateus Fernandes Reu Urban, Leandro Procopio, Renato Zangaro, Regiane Albertini

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Senescence changes include postural balance, inferring the risk of falls, and can lead to fractures, bedridden, and the risk of death. Physical activity, e.g., cardiovascular exercises, is notable for improving balance due to brain cell stimulations, but fine coordination exercises also elevate cell brain metabolism. This study aimed to verify whether the elderly person who performs fine motor activity has a balance similar to that of those who practice physical activity. The subjects were divided into three groups according to the activity practice: control group (CG) with seven participants for the sedentary individuals, motor coordination group (MCG) with six participants, and activity practitioner group (PAG) with eight participants. Data comparisons were from the Berg balance scale, Time up and Go test, and stabilometric analysis. Descriptive statistical and ANOVA analyses were performed for data analysis. The results reveal that including fine motor activities can improve the balance of the elderly and indirectly decrease the risk of falls.

Keywords: balance, barapodometer, coordination, elderly

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: R. Marandi, H. Shahrir, T. Nejad Ghaffar Borhani, M. Kamaruddin

Abstract:

In the present study, a steady state population balance model was developed to predict the polymer particle size distribution (PSD) in ethylene gas phase fluidized bed olefin polymerization reactors. The multilayer polymeric flow model (MPFM) was used to calculate the growth rate of a single polymer particle under intra-heat and mass transfer resistance. The industrial plant data were used to calculate the growth rate of polymer particle and the polymer PSD. Numerical simulations carried out to describe the influence of effective monomer diffusion coefficient, polymerization rate and initial catalyst size on the catalyst particle growth and final polymer PSD. The results present that the intra-heat and mass limitation is important for the ethylene polymerization, the growth rate of particle and the polymer PSD in the fluidized bed reactor. The effect of the agglomeration on the PSD is also considered. The result presents that the polymer particle size distribution becomes broader as the agglomeration exits.

Keywords: population balance, olefin polymerization, fluidized bed reactor, particle size distribution, agglomeration

Procedia PDF Downloads 310

Authors: Ayda Nikkar, Roghayye Ahmadiasl

Abstract:

In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

Procedia PDF Downloads 283

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

Procedia PDF Downloads 173

Authors: Onur Onder, Celal Tanuca, Mahir Ozil, Halil Sen, Alkım Ozkan, Engin Ceylan, Ali Istek, Ozgur Saglam

Abstract:

White balance adjustment of LCD TVs is an important procedure which has a direct influence on quality perception. Existing methods adjust RGB gain and offset values in different white levels during production. This paper suggests an iterative method in which the gamma is pre-adjusted during the design stage, and only 80% white is adjusted during production by modifying only RGB gain values (offset values are not modified). This method reduces the white balance adjustment time, contributing to the total efficiency of the production. Experiment shows that the adjustment results are well within requirements.

Keywords: color temperature, LCD panel deviation, LCD TV manufacturing, white balance

Procedia PDF Downloads 195