Pub Date : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34069
S. Khadka
The sequencing problem which minimizes the deviation between the actual (integral) and the ideal (rational) cumulative production of a variety of models of a common base product is called the product rate variation problem. If the objective is to minimize the maximum deviation, the problem is bottleneck product rate variation problem and the problem with the objective of minimizing all the deviations is the total product rate variation problem. The problem has been widely studied with several pseudo-polynomial time exact algorithms and heurism-tics. The lower bound of a feasible solution to the problem has been investigated to be tight. However, the upper bound of a feasible solution had been established in the literature which could further be improved. In this paper, we propose the improved upper bound for BPRVP and TPRVP.
{"title":"Improved Upper Bound to Product Rate Variation Problem","authors":"S. Khadka","doi":"10.3126/NMSR.V37I1-2.34069","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34069","url":null,"abstract":"The sequencing problem which minimizes the deviation between the actual (integral) and the ideal (rational) cumulative production of a variety of models of a common base product is called the product rate variation problem. If the objective is to minimize the maximum deviation, the problem is bottleneck product rate variation problem and the problem with the objective of minimizing all the deviations is the total product rate variation problem. The problem has been widely studied with several pseudo-polynomial time exact algorithms and heurism-tics. The lower bound of a feasible solution to the problem has been investigated to be tight. However, the upper bound of a feasible solution had been established in the literature which could further be improved. In this paper, we propose the improved upper bound for BPRVP and TPRVP.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133888542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34063
I. Adhikari, T. N. Dhamala
Evacuation planning problem deals with sending the maximum number of evacuees from the danger zone to the safe zone in minimum time as eciently as possible. The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem. Bus based evacuation planning problem (BEPP), as an important variant of the vehicle routing problem (VRP), is one of the emerging evacuation planning problems. In this work, an organized overview of this problem with a focus on their solution status is compactly presented. Arrival patterns of the evacuees including their transshipments at different pickup locations and their assignments are presented. Finally, a BEPP model and a solution for a special network are also proposed.
{"title":"On the Transit-Based Evacuation Strategies in an Integrated Network Topology","authors":"I. Adhikari, T. N. Dhamala","doi":"10.3126/NMSR.V37I1-2.34063","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34063","url":null,"abstract":"Evacuation planning problem deals with sending the maximum number of evacuees from the danger zone to the safe zone in minimum time as eciently as possible. The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem. Bus based evacuation planning problem (BEPP), as an important variant of the vehicle routing problem (VRP), is one of the emerging evacuation planning problems. In this work, an organized overview of this problem with a focus on their solution status is compactly presented. Arrival patterns of the evacuees including their transshipments at different pickup locations and their assignments are presented. Finally, a BEPP model and a solution for a special network are also proposed.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122427096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34093
Puskar R. Pokhrel, Parameshwari Kattel, Khim B. Khattri, J. Kafle
Pokhrel et al. recently developed a generalized quasi two-phase bulk mixture model for mass flow. This model has been constructed by employing full dimensional two-phase mass flow model equations. The model is a set of coupled partial differential equations which is characterized by some new mechanical and dynamical aspects of generalized bulk and shear viscosities, pressure, velocities and effective friction for the mixture where all these are evolving as functions of several dynamical variables, physical parameters, inertial and dynamical coefficients and drift factors. They formulated pressure and rate-dependent Coulumbviscoplastic rheology of the mixture mass flow to describe the model equation. Rheological behavior of the flow dynamics affects the whole dynamics of mixture mass flow. So, in this paper, the relations of mixture pressure and viscosity with respect to pressure drifts and solid volume fractions are studied to describe the rheological behavior of the generalized bulk mixture mass flow model. Moreover, the behaviour of mixture viscosities with respect to isotrophic drifts are also analyzed. We also present the simulation result for the time evolution of the drift induced full dynamical mixture pressure of the material exited from a silo gate that moves down slope along a channel.
{"title":"Rheological Parameter Analysis in Generalized Bulk Mixture Mass Flow Model","authors":"Puskar R. Pokhrel, Parameshwari Kattel, Khim B. Khattri, J. Kafle","doi":"10.3126/NMSR.V37I1-2.34093","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34093","url":null,"abstract":"Pokhrel et al. recently developed a generalized quasi two-phase bulk mixture model for mass flow. This model has been constructed by employing full dimensional two-phase mass flow model equations. The model is a set of coupled partial differential equations which is characterized by some new mechanical and dynamical aspects of generalized bulk and shear viscosities, pressure, velocities and effective friction for the mixture where all these are evolving as functions of several dynamical variables, physical parameters, inertial and dynamical coefficients and drift factors. They formulated pressure and rate-dependent Coulumbviscoplastic rheology of the mixture mass flow to describe the model equation. Rheological behavior of the flow dynamics affects the whole dynamics of mixture mass flow. So, in this paper, the relations of mixture pressure and viscosity with respect to pressure drifts and solid volume fractions are studied to describe the rheological behavior of the generalized bulk mixture mass flow model. Moreover, the behaviour of mixture viscosities with respect to isotrophic drifts are also analyzed. We also present the simulation result for the time evolution of the drift induced full dynamical mixture pressure of the material exited from a silo gate that moves down slope along a channel.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127370833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-31DOI: 10.3126/nmsr.v36i1-2.29968
A. Meurer, A. Weber, H. Bart, A. Klar, S. Tiwari
We consider a simplified model for the simulation of suspended ellipsoidal particles in fluid flow presented in [1] and investigate the calibration of the model from lab size experiments. Data have been recorded using a camera set-up and post-processing of the pictures. The model uses a simplified description for the orientation and position of the particles based on Jeffery’s equation. Additionally, particle-particle interaction and particle-wall interaction are taken into account.
{"title":"Experimental Validation of a Microscopic Ellipsoidal Interacting Particle Model Immersed in Fluid Flow","authors":"A. Meurer, A. Weber, H. Bart, A. Klar, S. Tiwari","doi":"10.3126/nmsr.v36i1-2.29968","DOIUrl":"https://doi.org/10.3126/nmsr.v36i1-2.29968","url":null,"abstract":"We consider a simplified model for the simulation of suspended ellipsoidal particles in fluid flow presented in [1] and investigate the calibration of the model from lab size experiments. Data have been recorded using a camera set-up and post-processing of the pictures. The model uses a simplified description for the orientation and position of the particles based on Jeffery’s equation. Additionally, particle-particle interaction and particle-wall interaction are taken into account.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130326556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-31DOI: 10.3126/nmsr.v36i1-2.29967
K. Luitel, D. B. Gurung, H. Khanal, K. N. Uprety
The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convection, radiation, and evaporation. The mode of heat transfer between the body and environment depends upon the human internal physiological phenomena, together with the boundary conditions. The present paper provides the comprehensive overview of the thermoregulatory system of human body and studies the numerical solution of unsteady-state one dimensional Pennes bio-heat equation with appropriate boundary conditions. The solution is used to observe the temperature profiles at different thermal conductivities, and different heat transfer coefficients in the living tissue at the various time steps. Various physical and physiological factors across the cylindrical living tissue have been incorporated in the model.
{"title":"Numerical Study of Transient Bio-Heat Transfer Model With Heat Transfer Coefficient and Conduction Effect in Cylindrical Living Tissue","authors":"K. Luitel, D. B. Gurung, H. Khanal, K. N. Uprety","doi":"10.3126/nmsr.v36i1-2.29967","DOIUrl":"https://doi.org/10.3126/nmsr.v36i1-2.29967","url":null,"abstract":"The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convection, radiation, and evaporation. The mode of heat transfer between the body and environment depends upon the human internal physiological phenomena, together with the boundary conditions. The present paper provides the comprehensive overview of the thermoregulatory system of human body and studies the numerical solution of unsteady-state one dimensional Pennes bio-heat equation with appropriate boundary conditions. The solution is used to observe the temperature profiles at different thermal conductivities, and different heat transfer coefficients in the living tissue at the various time steps. Various physical and physiological factors across the cylindrical living tissue have been incorporated in the model.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125873169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-31DOI: 10.3126/nmsr.v36i1-2.29970
Urmila Pyakurel
In this paper, we investigate the minimum cost flow problem in two terminal series parallel network. We present modified minimum cost flow algorithm that computes the maximum dynamic and the earliest arrival flows in strongly polynomial time and also preserves all unused arc capacities. We also present strongly polynomial time minimum cost partial contraflow algorithm that solves both problems with partial reversals of arc capacities on two terminal series parallel networks.
{"title":"Efficient algorithm for Minimum cost flow problem with partial lane reversals","authors":"Urmila Pyakurel","doi":"10.3126/nmsr.v36i1-2.29970","DOIUrl":"https://doi.org/10.3126/nmsr.v36i1-2.29970","url":null,"abstract":"In this paper, we investigate the minimum cost flow problem in two terminal series parallel network. We present modified minimum cost flow algorithm that computes the maximum dynamic and the earliest arrival flows in strongly polynomial time and also preserves all unused arc capacities. We also present strongly polynomial time minimum cost partial contraflow algorithm that solves both problems with partial reversals of arc capacities on two terminal series parallel networks.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"13 Odontol Sect 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116539259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-13DOI: 10.3126/nmsr.v36i1-2.29969
S. Pathak
In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in Rn for n ≥ 3 with smooth periodic initial data and derive a priori estimtes of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a special case of a paper by H-O Kreiss and J. Lorenz which also generalizes the main result of their paper to higher dimension.
{"title":"A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations with periodic initial data","authors":"S. Pathak","doi":"10.3126/nmsr.v36i1-2.29969","DOIUrl":"https://doi.org/10.3126/nmsr.v36i1-2.29969","url":null,"abstract":"In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in Rn for n ≥ 3 with smooth periodic initial data and derive a priori estimtes of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a special case of a paper by H-O Kreiss and J. Lorenz which also generalizes the main result of their paper to higher dimension.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132308991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.3126/nmsr.v35i1-2.29977
Dilip Gurung
Mathematical formulation for heat transfer in living tissue is different than an inert material, and is a current growing research interest area for many researchers due to its wide applications in many medical therapies and physiological studies. This interest stems from the rapid advancement of computational technology and advanced numerical mathematical techniques. The paper focuses on review on basic formulations of bio-heat equation proposed so far by several authors in the living tissue and its some applications.
{"title":"Bioheat Transfer Equation in Living Tissue and Some Applications","authors":"Dilip Gurung","doi":"10.3126/nmsr.v35i1-2.29977","DOIUrl":"https://doi.org/10.3126/nmsr.v35i1-2.29977","url":null,"abstract":"Mathematical formulation for heat transfer in living tissue is different than an inert material, and is a current growing research interest area for many researchers due to its wide applications in many medical therapies and physiological studies. This interest stems from the rapid advancement of computational technology and advanced numerical mathematical techniques. The paper focuses on review on basic formulations of bio-heat equation proposed so far by several authors in the living tissue and its some applications.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128495346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.3126/nmsr.v35i1-2.29974
R. Dhungana, T. N. Dhamala
The abstract flow model is the generalization of network flow model which deals with the flow paths (routes) satisfying the switching property. Contraflow model increases the flow value by reversing the required arc directions from the sources to the sinks. In this paper, we integrate the concepts of abstract flow and contraflow to introduce abstract earliest arrival transshipment contraflow model in multi-terminal abstract network. The abstract contraflow on multi-terminal dynamic network is NP-Complete. We present an efficient approximation algorithm to solve the problem. This approach satisfies the demand of sinks by sending optimal flow at every possible time point and seeks to eliminate the crossing conflicts.
{"title":"Abstract Earliest Arrival Transshipment with Network Reconfiguration","authors":"R. Dhungana, T. N. Dhamala","doi":"10.3126/nmsr.v35i1-2.29974","DOIUrl":"https://doi.org/10.3126/nmsr.v35i1-2.29974","url":null,"abstract":"The abstract flow model is the generalization of network flow model which deals with the flow paths (routes) satisfying the switching property. Contraflow model increases the flow value by reversing the required arc directions from the sources to the sinks. In this paper, we integrate the concepts of abstract flow and contraflow to introduce abstract earliest arrival transshipment contraflow model in multi-terminal abstract network. The abstract contraflow on multi-terminal dynamic network is NP-Complete. We present an efficient approximation algorithm to solve the problem. This approach satisfies the demand of sinks by sending optimal flow at every possible time point and seeks to eliminate the crossing conflicts.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114616020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.3126/nmsr.v35i1-2.29978
C. Kanchana, P. Siddheshwar
In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.
{"title":"Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations","authors":"C. Kanchana, P. Siddheshwar","doi":"10.3126/nmsr.v35i1-2.29978","DOIUrl":"https://doi.org/10.3126/nmsr.v35i1-2.29978","url":null,"abstract":"In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124946247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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