Search results for: water balance equation

Authors: Yusuf, S. I., Saba, A., Olaoye, D. O., Ibrahim J. A., Yahaya H. M., Jatto A. O

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Nuclear Magnetic Resonance (NMR) technology has been applied in several ways to provide vital information about petro-physical properties of reservoirs. However, due to the need to study the molecular behaviours of particles of the fluids in different restricted media, diffusion magnetic resonance equation is hereby applied in spherical coordinates and solved analytically using the method of separation of variables and solution of Legendre equation by Frobenius method. The viscous fluid considered in this research work is unused oil while the non-viscous fluid is water. The results obtained show that water begins to manifest appreciable change at radial adjustment value of 10 and Magnetization of 2.31191995400015x1014 and relaxes finally at 2.30x1014 at radial adjustment value of 1. On the other hand, unused engine oil begins to manifest its changes at radial adjustment value of 40 and Magnetization of 1.466557018x1014and relaxes finally at 1.48x1014 at radial adjustment value of 5.

Keywords: viscous and non-viscous fluid, restricted medium, relaxation times, coefficient of diffusion

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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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: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

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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: Irvan Adhin Cholilie, Susinggih Wijana, Yusron Sugiarto

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The aim of this research is to compare the results of black grass jelly produced using laboratory scale and double scale. In this research, the production from the laboratory scale is using ingredients of 1 kg black grass jelly added with 5 liters of water, while the double scale is using 5 kg black grass jelly and 75 liters of water. The results of organoleptic tests performed by 30 panelists (general) to the sample gels of grass black powder produced from both of laboratory and double scale are not different significantly in color, odor, flavor, and texture. Proximate test results conducted in both of grass black jelly powder produced in laboratory scale and double scale also have no significant differences in all parameters. Grass black jelly powder from double scale contains water, carbohydrate, crude fiber, and yield in the amount of 12,25 %; 43,7 %; 5,89 %; and 16,28 % respectively. The results of the energy efficiency analysis by boiling, draining, evaporation, drying, and milling processes are 85,11 %; 76,97 %; 99,64 %; 99,99% and 99,39% respectively. The utility needs including water needs for each batch amounted 0.1 m3 and cost Rp 220,5 per batch, the electricity needs for each batch is 20.01 kWh and cost Rp 18569.28 per batch, and LPG needs for each batch is 30 kg costed Rp 234,000.00 so that the total cost spent for the process is Rp 252,789.78 .

Keywords: black grass jelly, powder, mass balance, energy balance, cost

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Authors: Rose-Michelle Smith, Musandji Fuamba, Salomon Salumu

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Water is vital for life. Access to drinking water and sanitation for humans is one of the Sustainable Development Goals (specifically the sixth) approved by United Nations Member States in September 2015. There are various problems identified relating to water: insufficient fresh water, inequitable distribution of water resources, poor water management in certain places on the planet, detection of water-borne diseases due to poor water quality, and the negative impacts of climate change on water. One of the major challenges in the world is finding ways to ensure that people and the environment have enough water resources to sustain and support their existence. Thus, this research project aims to develop a tool to assess the availability, quality and needs of water in current and future situations with regard to climate change. This tool was tested using threshold values for three regions in three countries: the Metropolitan Community of Montreal (Canada), Normandie Region (France) and North Department (Haiti). The WEAP software was used to evaluate the available quantity of water resources. For water quality, two models were performed: the Canadian Council of Ministers of the Environment (CCME) and the Malaysian Water Quality Index (WQI). Preliminary results showed that the ratio of the needs could be estimated at 155, 308 and 644 m3/capita in 2023 for Normandie, Cap-Haitian and CMM, respectively. Then, the Water Quality Index (WQI) varied from one country to another. Other simulations regarding the water availability and quality are still in progress. This tool will be very useful in decision-making on projects relating to water use in the future; it will make it possible to estimate whether the available resources will be able to satisfy the needs.

Keywords: climate change, water needs, balance sheet, water quality

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Authors: Kunihisa Kakumoto

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Purpose: The global environmental problem is now raised in the global dimension. The sprawl phenomenon over the natural limitation is to be made a forecast beforehand in an algorithmic way so that the condition of our social life can hopefully be protected under the natural limitation. The sustainable condition in the globe is now to be found to keep the balance between the capacity of nature and the possibility of our social lives. The amount of water on the earth is limited. Therefore, on the reason, sustainable conditions are strongly dependent on the capacity of water. The amount of water can be considered in relation to the area of the green planting because a certain volume of the water can be obtained in the forest, where the green planting can be preserved. We can find the sustainable conditions of the water in relation to the green planting area. The reduction of CO₂ by green planting is also possible. Possible Measure and the Methods: Until now, by the opportunity of many international conferences, the concept of the solar community as one prototype has been introduced by technical papers. The algorithmic trial calculation on the basic concept of the solar community can be taken into consideration. The concept of the solar community is based on the collected data of the solar model house. According to the algorithmic results of the prototype, the simulation work in the globe can be performed as the algorithmic conversion results. This algorithmic study can be simulated by the amount of water, also in relation to the green planting area. Additionally, the submission of CO₂ in the solar community and the reduction of CO₂ by green planting can be calculated. On the base of these calculations in the solar community, the sustainable conditions on the globe can be simulated as the conversion results in an algorithmic way. The digital formation in the solar community can also be taken into consideration by this opportunity. Conclusion: For the finding of sustainable conditions around the globe, the solar community as one prototype has been taken into consideration. The role of the water is very important because the capacity of the water supply is very limited. But, at present, the cycle of the social community is not composed by the point of the natural mechanism. The simulative calculation of this study can be shown by the limitation of the total water supply. According to this process, the total capacity of the water supply and the capable residential number of the population and the areas can be taken into consideration by the algorithmic calculation. For keeping enough water, the green planting areas are very important. The planting area is also very important to keep the balance of CO₂. The simulative calculation can be performed by the relation between the submission and the reduction of CO₂ in the solar community. For the finding of this total balance and the sustainable conditions, the green planting area and the total amount of water can be recognized by the algorithmic simulative calculation. The study for the finding of sustainable conditions can be performed by the simulative calculations on the algorithmic model in the solar community as one prototype. The example of one prototype can be in balance. The activity of the social life must be in the capacity of the natural mechanism. The capable capacity of the natural environment in our world is very limited.

Keywords: the solar community, the sustainable condition, the natural limitation, the algorithmic calculation

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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: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding

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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: 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: 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: Mohamed Amine Helali, Walid Oueslati, Ayed Added

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Sedimentation rates and total fluxes of heavy metals (Fe, Mn, Pb, Zn and Cu) was measured in three different depths (10m, 20m and 40m) during March and August 2012, offshore of the Mejerda River outlet (Gulf of Tunis, Tunisia). The sedimentation rates are estimated from the fluxes of the suspended particulate matter at 7.32, 5.45 and 4.39 mm y⁻¹ respectively at 10m, 20m and 40m depth. Heavy metals sequestration in sediments was determined by chemical speciation and the total metal contents in each core collected from 10, 20 and 40m depth. Heavy metals intake to the sediment was measured also from the suspended particulate matter, while the fluxes from the sediment to the water column was determined using the benthic chambers technique and from the diffusive fluxes in the pore water. Results shown that iron is the only metal for which the balance transfer between intake/uptake (45 to 117 / 1.8 to 5.8 g m² y⁻¹) and sequestration (277 to 378 g m² y⁻¹) was negative, at the opposite of the Lead which intake fluxes (360 to 480 mg m² y⁻¹) are more than sequestration fluxes (50 to 92 mg m² y⁻¹). The balance transfer is neutral for Mn, Zn, and Cu. These clearly indicate that the contributions of Mejerda have consistently varied over time, probably due to the migration of the River mouth and to the changes in the mining activity in the Mejerda catchment and the recent human activities which affect the delta area.

Keywords: delta, fluxes, heavy metals, sediments, sedimentation rates

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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: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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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: Muhammad Tayyab Afzal, Muhammad Arslan, Mirza Muhammad Waqar

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One of the key components of the water cycle is evapotranspiration (ET), which represents water consumption by vegetated and non-vegetated surfaces. Conventional techniques for measurements of ET are point based and representative of the local scale only. Satellite remote sensing data with large area coverage and high temporal frequency provide representative measurements of several relevant biophysical parameters required for estimation of ET at regional scales. The objective is of this research is to exploit satellite data in order to estimate evapotranspiration. This study uses Surface Energy Balance System (SEBS) model to calculate daily actual evapotranspiration (ETa) in Larkana District, Sindh Pakistan using Landsat TM data for clouds-free days. As there is no flux tower in the study area for direct measurement of latent heat flux or evapotranspiration and sensible heat flux, therefore, the model estimated values of ET were compared with reference evapotranspiration (ETo) computed by FAO-56 Penman Monteith Method using meteorological data. For a country like Pakistan, agriculture by irrigation in the river basins is the largest user of fresh water. For the better assessment and management of irrigation water requirement, the estimation of consumptive use of water for agriculture is very important because it is the main consumer of water. ET is yet an essential issue of water imbalance due to major loss of irrigation water and precipitation on cropland. As large amount of irrigated water is lost through ET, therefore its accurate estimation can be helpful for efficient management of irrigation water. Results of this study can be used to analyse surface conditions, i.e. temperature, energy budgets and relevant characteristics. Through this information we can monitor vegetation health and suitable agricultural conditions and can take controlling steps to increase agriculture production.

Keywords: SEBS, remote sensing, evapotranspiration, ETa

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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: 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: 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: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

Abstract:

The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

Procedia PDF Downloads 80

Authors: Ayobami Solomon Popoola

Abstract:

Yam is majorly a carbohydrate food grown in most parts of the world. It could be boiled, fried or roasted for consumption in a variety of ways. Blanching is an established heat pre-treatment given to fruits and vegetables prior to further processing such as dehydration, canning, freezing etc. Losses of soluble solids during blanching has been a great problem because a reasonable quantity of the water-soluble nutrients are inevitably leached into the blanching water. Without blanching, the high residual levels of reducing sugars after extended storage produce a dark, bitter-tasting product because of the Maillard reactions of reducing sugars at frying temperature. Measurement and prediction of such losses are necessary for economic efficiency in production and to establish the level of effluent treatment of the blanching water. This paper aims at resolving this problem by investigating the effects of cube size and temperature on the rate of diffusional losses of reducing sugars and total sugars during hot water blanching of water-yam. The study was carried out using four temperature levels (65, 70, 80 and 90 °C) and two cubes sizes (0.02 m³ and 0.03 m³) at 4 times intervals (5, 10, 15 and 20 mins) respectively. Obtained data were fitted into Fick’s non-steady equation from which diffusion coefficients (Da) were obtained. The Da values were subsequently fitted into Arrhenius plot to obtain activation energies (Ea-values) for diffusional losses. The diffusion co-efficient were independent of cube size and time but highly temperature dependent. The diffusion coefficients were ≥ 1.0 ×10⁻⁹ m²s⁻¹ for reducing sugars and ≥ 5.0 × 10⁻⁹ m²s⁻¹ for total sugars. The Ea values ranged between 68.2 to 73.9 KJmol⁻¹ and 7.2 to 14.30 KJmol⁻¹ for reducing sugars and total sugars losses respectively. Predictive equations for estimating amount of reducing sugars and total sugars with blanching time of water-yam at various temperatures were also presented. The equation could be valuable in process design and optimization. However, amount of other soluble solids that might have leached into the water along with reducing and total sugars during blanching was not investigated in the study.

Keywords: blanching, kinetics, sugar losses, water yam

Procedia PDF Downloads 165

Authors: Ognjen Vukovic

Abstract:

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

Procedia PDF Downloads 473