This paper presents a simple, low cost measurement technique that involves use of a Force Sensing... more This paper presents a simple, low cost measurement technique that involves use of a Force Sensing Resistor placed over the patient's chest to record chest movements and hence record the breathing signal. Analysis of the obtained Breathing signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of central sleep apnea, which may reduce the need for uncomfortable sleep studies. The proposed method involves using Wavelet Transform based feature extraction, followed by classification using Least Square Support Vector Machine . A 95% true detection rate was obtained using the proposed method. Finally, a real time breathing monitoring and Central Sleep Apnea diagnosis system is built using the proposed method.
Hierarchical computational schemes based on tube theories enable calculation of rheological prope... more Hierarchical computational schemes based on tube theories enable calculation of rheological properties for polymers of arbitrary topology. In this study, such a scheme is used to systematically explore key rheological features of model long-chain branched systems. Empirical relations between molecular structure and rheology typically use overall molar mass and branching averages as structural variables, due to lack of knowledge on details of the topological structure or to limited structural variability between available experimental samples. The present approach clarifies the effect of additional structural variation beyond overall molar mass and branching level. For the polymer structures under consideration, arm length is found to dominate zero-shear viscosity, whereas the recoverable compliance scales with the ratio of total molar mass and backbone molar mass. Different topologies are found to lead to a different shear thinning/elasticity balance. The simulation approach provides clear hints for polymer designers that look to obtain specific property balances via topological modifications. This complements the classical empirical approach. Merging the different approaches is expected to synergistically speed up new product development.
We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (20... more We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (2006)] for predicting the linear rheology of arbitrarily branched polymer melts, which was successfully used for well defined architectures (stars, combs, Cayley trees etc.) and well-characterised industrial resins. We now discuss an extension to the non-linear regime, via a mapping onto a multi-mode ``pom-pom" ensemble. There is, in principle, sufficient information in the algorithm to do this without additional free parameters. However, the procedure is not exact and one must consider the most important physics to represent. In particular, we highlight the need to distinguish between stress relaxation via constraint release and via tube escape. We also discuss the topological ``priority" variable (which limits the stress in extension) and the considerations needed when assigning this to each polymer strand (which polymer segments should one count as relaxed?) In doing this, and as a result of tube advection, we find we need to introduce a new variable (``altitude") related to the topological distance of a strand from the molecule centre.
In recent years the association between molecular structure and linear rheology has been establis... more In recent years the association between molecular structure and linear rheology has been established and well-understood through the tube concept and its extensions for well-characterized materials (e.g. McLeish, Adv. Phys. 2002). However, for industrial branched polymeric material at processing conditions this piece of information is missing. A large number of phenomenological models have been developed to describe the nonlinear response of polymers. But none of these models takes into account the underlying molecular structure, leading to a fitting procedure with arbitrary fitting parameters. The goal of applied molecular rheology is a predictive scheme that runs in its entirety from the molecular structure from the reactor to the non-linear rheology of the resin. In our approach, we use a model for the industrial reactor to explicitly generate the molecular structure ensemble of LDPE's, (Tobita, J. Polym. Sci. B 2001), which are consistent with the analytical information. We calculate the linear rheology of the LDPE ensemble with the use of a tube model for branched polymers (Das et al., J. Rheol. 2006). We then, separate the contribution of the stress decay to a large number of pompom modes (McLeish et al., J. Rheol. 1998 & Inkson et al., J. Rheol. 1999) with the stretch time and the priority variables corresponding to the actual ensemble of molecules involved. This multimode pompom model allows us to predict the nonlinear properties without any fitting parameter. We present and analyze our results in comparison with experimental data on industrial materials.
We present a predictive scheme connecting the topological structure of highly branched entangled ... more We present a predictive scheme connecting the topological structure of highly branched entangled polymers, with industrial-level complexity, to the emergent viscoelasticity of the polymer melt. The scheme is able to calculate the linear and nonlinear viscoelasticity of a stochastically branched “high-pressure free radical” polymer melt as a function of the chemical kinetics of its formation. The method combines numerical simulation of polymerization with the tube/entanglement physics of polymer dynamics extended to fully nonlinear response. We compare calculations for a series of low-density polyethylenes with experiments on structural and viscoelastic properties. The method provides a window onto the molecular processes responsible for the optimized rheology of these melts, connecting fundamental science to process in complex flow, and opens up the in silico design of new materials.
We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan [P... more We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the “rheologically relevant” linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior—which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value.
We present a general algorithm for predicting the linear rheology of branched polymers. While the... more We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocenecatalyzed polyethylene resins. Application of our algorithm shows the importance of branch-onbranch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.
The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo ... more The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo simulation in the two cases of a batch and a semibatch reactor. The algorithm we develop can be applied, in principle, to an arbitrary number of catalysts with different propensities toward the formation of long chain branches. We compare our model to an experimental two-catalyst system, in which one of the catalysts makes only linear chains and the ratio of the two catalysts is varied, to synthesize a series of different molar mass resins. Results from our simulations show good agreement with experimentally measured molecular weight distributions, the ratio of unsaturated to saturated chain ends (found by 13 C NMR) and the number of branches per 10000C. We also examine the effect on the amount of branching when molecular hydrogen gas is added to the system to act as a chain transfer agent.
We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et... more We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. (PRE, 60, 5657, 1999) to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed by Lusignan et al. are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the `rheologically relevant' linear segment length is smaller than that estimated by them. We use a numerical method based on tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior - which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches Rouse-like value.
The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo ... more The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo simulation in the two cases of a batch and a semibatch reactor. The algorithm we develop can be applied, in principle, to an arbitrary number of catalysts with different propensities toward the formation of long chain branches. We compare our model to an experimental two-catalyst system, in which one of the catalysts makes only linear chains and the ratio of the two catalysts is varied, to synthesize a series of different molar mass resins. Results from our simulations show good agreement with experimentally measured molecular weight distributions, the ratio of unsaturated to saturated chain ends (found by 13 C NMR) and the number of branches per 10000C. We also examine the effect on the amount of branching when molecular hydrogen gas is added to the system to act as a chain transfer agent.
We present the synthesis of polystyrene combs via an improved procedure, which allows the average... more We present the synthesis of polystyrene combs via an improved procedure, which allows the average number of arms to be small (3-5) but well controlled. It is shown that Temperature Gradient Interaction Chromatography (TGIC) proves to be a highly effective method for the analysis of these combs, providing directly the distribution of the number of arms on the synthesised comb molecules. We use this arm-number distribution to model the linear rheology of an entangled melt of such combs, via our previously-published algorithm [Das et al, J. Rheology 2006, 50, 207-234], and demonstrate that this compares favourably with the measured linear rheology. A comparison is also made with the predicted rheology for two alternative assumptions about the distribution of arms on the comb, (i) where it is assumed that the addition of arms is an ideal random process, and (ii) where there is a fixed number of arms per comb. These predictions also agree well with the experimental results, thus supporting the validity of simpler analytical approaches based on constant arm-number, at least for the arm-number distribution considered here.
Breakdown threshold voltage of an electrode less toroidal discharge has been studied using H-type... more Breakdown threshold voltage of an electrode less toroidal discharge has been studied using H-type solenoid coil excited by a 13.56 MHz radio frequency power in absence and in presence of a toroidal error field with different pressures, and axial magnetic field for dry air. The breakdown threshold depends on various filling parameters e.g. error field , and magnetic field. Again the floating double probe technique was used to measure the plasma temperature and density in presence of error field using the equivalent resistance method [1,2,3,4,5] for dry air. all measurements were made in a 13.56 mhz inductively coupled radio frequency plasma discharge at different pressures ranging from 0.07 torr to 0.20 torr and magnetic field was varied between 0g to 75g.
In the present work, the floating double probe technique was used to determine the plasma paramet... more In the present work, the floating double probe technique was used to determine the plasma parameters by using the equivalent resistance method [1,2,3,4,5] for hydrogen in toroidal discharge. Measurements were done for transverse and longitudinal positions of the probes to the axial toroidal magnetic field. The experiment was carried out in a 13.56 MHz inductively coupled radio frequency plasma discharge at different pressures of 0.07 torr to 0.20 torr and magnetic fields of 0G to 75G and observed the differences of plasma temperature and particle number density on the discharge axis of the torus. It is also observed that the plasma temperature decreases where as the plasma radial density increases for axial positions but for transverse positions of the probes, the plasma temperature increases and the radial density decreases with the magnetic field and changes with pressure also. The results were compared with nitrogen and argon as well as with direct current glow discharge plasmas with identical input magnetic field [6]. The validity of the probe method for measurement of plasma temperature and density in a toroidal discharge has been discussed.
In the present work, the floating double probe technique was used to determine the plasma paramet... more In the present work, the floating double probe technique was used to determine the plasma parameters by using the equivalent resistance method [1,2,3,4,5] for hydrogen in toroidal discharge. Measurements were done for transverse and longitudinal positions of the probes to the axial toroidal magnetic field. The experiment was carried out in a 13.56 MHz inductively coupled radio frequency plasma discharge at different pressures of 0.07 torr to 0.20 torr and magnetic fields of 0G to 75G and observed the differences of plasma temperature and particle number density on the discharge axis of the torus. It is also observed that the plasma temperature decreases where as the plasma radial density increases for axial positions but for transverse positions of the probes, the plasma temperature increases and the radial density decreases with the magnetic field and changes with pressure also. The results were compared with nitrogen and argon as well as with direct current glow discharge plasmas with identical input magnetic field [6]. The validity of the probe method for measurement of plasma temperature and density in a toroidal discharge has been discussed.
Abstract We develop a variational theory of hot dense matter which generalizes the zero temperatu... more Abstract We develop a variational theory of hot dense matter which generalizes the zero temperature variational methods to finite temperatures without any orthogonality corrections. This method can be used to calculate the equation of state for matter in supernovae, ...
Supernova matter consisting of protons, neutrons and electrons with proton fraction yp = 0.3 are ... more Supernova matter consisting of protons, neutrons and electrons with proton fraction yp = 0.3 are studied within finite temperature Brueckner-Goldstone approach with effective two-body Sussex interaction for various values of densities and at temperatures T = 5, 7 and 10 MeV. It is found that at a given density, temperature and proton fraction, the entropy production, internal energy per nucleon, free energy per nucleon and pressure generated by protons and electrons are not equal. Entropy produced in the supernova matter is larger than that of corresponding asymmetric nuclear matter. The rise in temperature with densities in this matter under adiabatic condition is relatively suppressed with respect to corresponding asymmetric nuclear matter. Contribution to internal energy and free energy due to electron components is more pronounced than those of nuclear components. But the contribution to entropy and pressure due to nuclear components is larger than those of electron components. It is observed that for the matter with proton fraction yp = 0.1, the internal energy, free energy and pressure generated due to protons are density-independent whereas, for supernova matter, these quantities are density-dependent. Distribution function, fraction of particles and mean field are the key factors to explain the characteristic properties of the constituent particles of supernova matter.
ABSTRACT The temperature dependence of different thermodynamic quantities such as the free energy... more ABSTRACT The temperature dependence of different thermodynamic quantities such as the free energy, chemical potential, symmetry energy, single particle potential, equation of state, etc., is studied for asymmetric nuclear matter within a fully self-consistent model with an effective interaction. The equation of state is found to be quite soft in agreement with supernova calculations. The critical temperature for the occurrence of a liquid gas phase transition is found to decrease with the proton to neutron ratio gamma and finally vanishes for pure neutron matter. The possibility of pi- condensation has also been studied.
Abstract We develop a variational theory of hot dense matter which generalizes the zero temperatu... more Abstract We develop a variational theory of hot dense matter which generalizes the zero temperature variational methods to finite temperatures without any orthogonality corrections. This method can be used to calculate the equation of state for matter in supernovae, ...
... 13 Natalie Drive, Hampton, Virginia 23660 R. Sahu Physics Department, Berhampur University, B... more ... 13 Natalie Drive, Hampton, Virginia 23660 R. Sahu Physics Department, Berhampur University, Berhampur 760 007, India (Received 20 September 1991) The ... However, Haar and Malfliet [12,13] had per-formed a fully self-consistent Dirac-Brueckner calcula-tion and found the ...
This paper presents a simple, low cost measurement technique that involves use of a Force Sensing... more This paper presents a simple, low cost measurement technique that involves use of a Force Sensing Resistor placed over the patient's chest to record chest movements and hence record the breathing signal. Analysis of the obtained Breathing signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of central sleep apnea, which may reduce the need for uncomfortable sleep studies. The proposed method involves using Wavelet Transform based feature extraction, followed by classification using Least Square Support Vector Machine . A 95% true detection rate was obtained using the proposed method. Finally, a real time breathing monitoring and Central Sleep Apnea diagnosis system is built using the proposed method.
Hierarchical computational schemes based on tube theories enable calculation of rheological prope... more Hierarchical computational schemes based on tube theories enable calculation of rheological properties for polymers of arbitrary topology. In this study, such a scheme is used to systematically explore key rheological features of model long-chain branched systems. Empirical relations between molecular structure and rheology typically use overall molar mass and branching averages as structural variables, due to lack of knowledge on details of the topological structure or to limited structural variability between available experimental samples. The present approach clarifies the effect of additional structural variation beyond overall molar mass and branching level. For the polymer structures under consideration, arm length is found to dominate zero-shear viscosity, whereas the recoverable compliance scales with the ratio of total molar mass and backbone molar mass. Different topologies are found to lead to a different shear thinning/elasticity balance. The simulation approach provides clear hints for polymer designers that look to obtain specific property balances via topological modifications. This complements the classical empirical approach. Merging the different approaches is expected to synergistically speed up new product development.
We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (20... more We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (2006)] for predicting the linear rheology of arbitrarily branched polymer melts, which was successfully used for well defined architectures (stars, combs, Cayley trees etc.) and well-characterised industrial resins. We now discuss an extension to the non-linear regime, via a mapping onto a multi-mode ``pom-pom" ensemble. There is, in principle, sufficient information in the algorithm to do this without additional free parameters. However, the procedure is not exact and one must consider the most important physics to represent. In particular, we highlight the need to distinguish between stress relaxation via constraint release and via tube escape. We also discuss the topological ``priority" variable (which limits the stress in extension) and the considerations needed when assigning this to each polymer strand (which polymer segments should one count as relaxed?) In doing this, and as a result of tube advection, we find we need to introduce a new variable (``altitude") related to the topological distance of a strand from the molecule centre.
In recent years the association between molecular structure and linear rheology has been establis... more In recent years the association between molecular structure and linear rheology has been established and well-understood through the tube concept and its extensions for well-characterized materials (e.g. McLeish, Adv. Phys. 2002). However, for industrial branched polymeric material at processing conditions this piece of information is missing. A large number of phenomenological models have been developed to describe the nonlinear response of polymers. But none of these models takes into account the underlying molecular structure, leading to a fitting procedure with arbitrary fitting parameters. The goal of applied molecular rheology is a predictive scheme that runs in its entirety from the molecular structure from the reactor to the non-linear rheology of the resin. In our approach, we use a model for the industrial reactor to explicitly generate the molecular structure ensemble of LDPE's, (Tobita, J. Polym. Sci. B 2001), which are consistent with the analytical information. We calculate the linear rheology of the LDPE ensemble with the use of a tube model for branched polymers (Das et al., J. Rheol. 2006). We then, separate the contribution of the stress decay to a large number of pompom modes (McLeish et al., J. Rheol. 1998 & Inkson et al., J. Rheol. 1999) with the stretch time and the priority variables corresponding to the actual ensemble of molecules involved. This multimode pompom model allows us to predict the nonlinear properties without any fitting parameter. We present and analyze our results in comparison with experimental data on industrial materials.
We present a predictive scheme connecting the topological structure of highly branched entangled ... more We present a predictive scheme connecting the topological structure of highly branched entangled polymers, with industrial-level complexity, to the emergent viscoelasticity of the polymer melt. The scheme is able to calculate the linear and nonlinear viscoelasticity of a stochastically branched “high-pressure free radical” polymer melt as a function of the chemical kinetics of its formation. The method combines numerical simulation of polymerization with the tube/entanglement physics of polymer dynamics extended to fully nonlinear response. We compare calculations for a series of low-density polyethylenes with experiments on structural and viscoelastic properties. The method provides a window onto the molecular processes responsible for the optimized rheology of these melts, connecting fundamental science to process in complex flow, and opens up the in silico design of new materials.
We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan [P... more We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the “rheologically relevant” linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior—which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value.
We present a general algorithm for predicting the linear rheology of branched polymers. While the... more We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocenecatalyzed polyethylene resins. Application of our algorithm shows the importance of branch-onbranch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.
The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo ... more The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo simulation in the two cases of a batch and a semibatch reactor. The algorithm we develop can be applied, in principle, to an arbitrary number of catalysts with different propensities toward the formation of long chain branches. We compare our model to an experimental two-catalyst system, in which one of the catalysts makes only linear chains and the ratio of the two catalysts is varied, to synthesize a series of different molar mass resins. Results from our simulations show good agreement with experimentally measured molecular weight distributions, the ratio of unsaturated to saturated chain ends (found by 13 C NMR) and the number of branches per 10000C. We also examine the effect on the amount of branching when molecular hydrogen gas is added to the system to act as a chain transfer agent.
We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et... more We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. (PRE, 60, 5657, 1999) to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed by Lusignan et al. are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the `rheologically relevant' linear segment length is smaller than that estimated by them. We use a numerical method based on tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior - which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches Rouse-like value.
The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo ... more The synthesis of polyolefins with two metallocene catalysts is explored via a simple Monte Carlo simulation in the two cases of a batch and a semibatch reactor. The algorithm we develop can be applied, in principle, to an arbitrary number of catalysts with different propensities toward the formation of long chain branches. We compare our model to an experimental two-catalyst system, in which one of the catalysts makes only linear chains and the ratio of the two catalysts is varied, to synthesize a series of different molar mass resins. Results from our simulations show good agreement with experimentally measured molecular weight distributions, the ratio of unsaturated to saturated chain ends (found by 13 C NMR) and the number of branches per 10000C. We also examine the effect on the amount of branching when molecular hydrogen gas is added to the system to act as a chain transfer agent.
We present the synthesis of polystyrene combs via an improved procedure, which allows the average... more We present the synthesis of polystyrene combs via an improved procedure, which allows the average number of arms to be small (3-5) but well controlled. It is shown that Temperature Gradient Interaction Chromatography (TGIC) proves to be a highly effective method for the analysis of these combs, providing directly the distribution of the number of arms on the synthesised comb molecules. We use this arm-number distribution to model the linear rheology of an entangled melt of such combs, via our previously-published algorithm [Das et al, J. Rheology 2006, 50, 207-234], and demonstrate that this compares favourably with the measured linear rheology. A comparison is also made with the predicted rheology for two alternative assumptions about the distribution of arms on the comb, (i) where it is assumed that the addition of arms is an ideal random process, and (ii) where there is a fixed number of arms per comb. These predictions also agree well with the experimental results, thus supporting the validity of simpler analytical approaches based on constant arm-number, at least for the arm-number distribution considered here.
Breakdown threshold voltage of an electrode less toroidal discharge has been studied using H-type... more Breakdown threshold voltage of an electrode less toroidal discharge has been studied using H-type solenoid coil excited by a 13.56 MHz radio frequency power in absence and in presence of a toroidal error field with different pressures, and axial magnetic field for dry air. The breakdown threshold depends on various filling parameters e.g. error field , and magnetic field. Again the floating double probe technique was used to measure the plasma temperature and density in presence of error field using the equivalent resistance method [1,2,3,4,5] for dry air. all measurements were made in a 13.56 mhz inductively coupled radio frequency plasma discharge at different pressures ranging from 0.07 torr to 0.20 torr and magnetic field was varied between 0g to 75g.
In the present work, the floating double probe technique was used to determine the plasma paramet... more In the present work, the floating double probe technique was used to determine the plasma parameters by using the equivalent resistance method [1,2,3,4,5] for hydrogen in toroidal discharge. Measurements were done for transverse and longitudinal positions of the probes to the axial toroidal magnetic field. The experiment was carried out in a 13.56 MHz inductively coupled radio frequency plasma discharge at different pressures of 0.07 torr to 0.20 torr and magnetic fields of 0G to 75G and observed the differences of plasma temperature and particle number density on the discharge axis of the torus. It is also observed that the plasma temperature decreases where as the plasma radial density increases for axial positions but for transverse positions of the probes, the plasma temperature increases and the radial density decreases with the magnetic field and changes with pressure also. The results were compared with nitrogen and argon as well as with direct current glow discharge plasmas with identical input magnetic field [6]. The validity of the probe method for measurement of plasma temperature and density in a toroidal discharge has been discussed.
In the present work, the floating double probe technique was used to determine the plasma paramet... more In the present work, the floating double probe technique was used to determine the plasma parameters by using the equivalent resistance method [1,2,3,4,5] for hydrogen in toroidal discharge. Measurements were done for transverse and longitudinal positions of the probes to the axial toroidal magnetic field. The experiment was carried out in a 13.56 MHz inductively coupled radio frequency plasma discharge at different pressures of 0.07 torr to 0.20 torr and magnetic fields of 0G to 75G and observed the differences of plasma temperature and particle number density on the discharge axis of the torus. It is also observed that the plasma temperature decreases where as the plasma radial density increases for axial positions but for transverse positions of the probes, the plasma temperature increases and the radial density decreases with the magnetic field and changes with pressure also. The results were compared with nitrogen and argon as well as with direct current glow discharge plasmas with identical input magnetic field [6]. The validity of the probe method for measurement of plasma temperature and density in a toroidal discharge has been discussed.
Abstract We develop a variational theory of hot dense matter which generalizes the zero temperatu... more Abstract We develop a variational theory of hot dense matter which generalizes the zero temperature variational methods to finite temperatures without any orthogonality corrections. This method can be used to calculate the equation of state for matter in supernovae, ...
Supernova matter consisting of protons, neutrons and electrons with proton fraction yp = 0.3 are ... more Supernova matter consisting of protons, neutrons and electrons with proton fraction yp = 0.3 are studied within finite temperature Brueckner-Goldstone approach with effective two-body Sussex interaction for various values of densities and at temperatures T = 5, 7 and 10 MeV. It is found that at a given density, temperature and proton fraction, the entropy production, internal energy per nucleon, free energy per nucleon and pressure generated by protons and electrons are not equal. Entropy produced in the supernova matter is larger than that of corresponding asymmetric nuclear matter. The rise in temperature with densities in this matter under adiabatic condition is relatively suppressed with respect to corresponding asymmetric nuclear matter. Contribution to internal energy and free energy due to electron components is more pronounced than those of nuclear components. But the contribution to entropy and pressure due to nuclear components is larger than those of electron components. It is observed that for the matter with proton fraction yp = 0.1, the internal energy, free energy and pressure generated due to protons are density-independent whereas, for supernova matter, these quantities are density-dependent. Distribution function, fraction of particles and mean field are the key factors to explain the characteristic properties of the constituent particles of supernova matter.
ABSTRACT The temperature dependence of different thermodynamic quantities such as the free energy... more ABSTRACT The temperature dependence of different thermodynamic quantities such as the free energy, chemical potential, symmetry energy, single particle potential, equation of state, etc., is studied for asymmetric nuclear matter within a fully self-consistent model with an effective interaction. The equation of state is found to be quite soft in agreement with supernova calculations. The critical temperature for the occurrence of a liquid gas phase transition is found to decrease with the proton to neutron ratio gamma and finally vanishes for pure neutron matter. The possibility of pi- condensation has also been studied.
Abstract We develop a variational theory of hot dense matter which generalizes the zero temperatu... more Abstract We develop a variational theory of hot dense matter which generalizes the zero temperature variational methods to finite temperatures without any orthogonality corrections. This method can be used to calculate the equation of state for matter in supernovae, ...
... 13 Natalie Drive, Hampton, Virginia 23660 R. Sahu Physics Department, Berhampur University, B... more ... 13 Natalie Drive, Hampton, Virginia 23660 R. Sahu Physics Department, Berhampur University, Berhampur 760 007, India (Received 20 September 1991) The ... However, Haar and Malfliet [12,13] had per-formed a fully self-consistent Dirac-Brueckner calcula-tion and found the ...
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