Hiroki Fukagawa | Kyushu University (original) (raw)

Papers by Hiroki Fukagawa

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2008

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2009

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2010

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2011

arXiv: Fluid Dynamics, 2014

AbstractWe propose equations governing the dissolution in inhomogeneous temperature field in terms... more AbstractWe propose equations governing the dissolution in inhomogeneous temperature field in terms of thevariational principle. The derived equations clarify that the interface energy between solute and solventhas a significant effect on the process of the dissolution. The interface energy restrains the dissolution,and the moving interface involves the heat of dissolution. Introduction Dissolution is an important process and frequentlydiscussed in industry as well as in science. For ex-ample, the dissolution of supercritical CO 2 in inter-stitial water is one of the most crucial research top-ics in CO 2 capture and storage (CCS), which storesthe CO 2 into the deep underground in a geologicalrock formation. The CO 2 can be trapped in themicro-pore space as droplets surrounded by water.At this small scale, the contribution of the interfaceenergyto the total energyis consequential, and thuscomes into play. Various phase field models basedon free energies are often used to study the dynam-i...

arXiv: Fluid Dynamics, 2014

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle. The dynamics of the fluids satisfy the conservation laws of mass, momentum, angular momentum, and energy, and obey the second law of thermodynamics. By Noether’s theorem, these conservation laws are associated with the corresponding symmetries. On the other hand, the equation for entropy gives a nonholonomic constraint. Then Lagrangians and this nonholonomic constraint of the fluids satisfy these symmetries. The dynamics of fluid are given as a weak solution, minimizing an action subject to this constraint. For the existence of the weak solution, all the surface terms appearing in the variational calculus have to vanish with the aid of the nonholonomic constraint. In this study, we show that the equation for entropy is determined to be consist to “the second law of thermodynamics”, “the symmetries”, and “the necessary condition of the existence of the weak so...

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

Progress of Theoretical Physics, 2010

Progress of Theoretical Physics, 2012

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Nihon Butsuri Gakkaishi, 2017

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

We propose equations governing the dissolution in inhomogeneous temperature field in terms of the... more We propose equations governing the dissolution in inhomogeneous temperature field in terms of the variational principle. The derived equations clarify that the interface energy between solute and solvent has a significant effect on the process of the dissolution. The interface energy restrains the dissolution, and the moving interface involves the heat of dissolution.

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle.

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle. The dynamics of the fluids satisfy the conservation laws of mass, momentum, angular momentum, and energy, and obey the second law of thermodynamics. By Noether's theorem, these conservation laws are associated with the corresponding symmetries. On the other hand, the equation for entropy gives a nonholonomic constraint. Then Lagrangians and this nonholonomic constraint of the fluids satisfy these symmetries. The dynamics of fluid are given as a weak solution, minimizing an action subject to this constraint. For the existence of the weak solution, all the surface terms appearing in the variational calculus have to vanish with the aid of the nonholonomic constraint. In this study, we show that the equation for entropy is determined to be consist to "the second law of thermodynamics", "the symmetries", and "the necessary condition of the existence of the weak solution". Our method gives a general scheme to derive the equation of motion for fluids in inhomogeneous temperature, and gives an explanation of some nontrivial thermal effects on the rotation of liquid crystal, vaporization of a one component fluid, and dissolution of a two component fluid.

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Progress of Theoretical Physics, 2010

Equations for a perfect fluid can be obtained by means of the variational principle both in the L... more Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in the latter description. We give a simple explanation for these fields; they are introduced to fix both ends of a pathline in the variational calculus. This restriction is imposed in the former description, and should be imposed in the latter description. It is also shown that we can derive a canonical Hamiltonian formulation for a perfect fluid by regarding the velocity field as the input in the framework of control theory.

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2008

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2009

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2010

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2011

arXiv: Fluid Dynamics, 2014

AbstractWe propose equations governing the dissolution in inhomogeneous temperature field in terms... more AbstractWe propose equations governing the dissolution in inhomogeneous temperature field in terms of thevariational principle. The derived equations clarify that the interface energy between solute and solventhas a significant effect on the process of the dissolution. The interface energy restrains the dissolution,and the moving interface involves the heat of dissolution. Introduction Dissolution is an important process and frequentlydiscussed in industry as well as in science. For ex-ample, the dissolution of supercritical CO 2 in inter-stitial water is one of the most crucial research top-ics in CO 2 capture and storage (CCS), which storesthe CO 2 into the deep underground in a geologicalrock formation. The CO 2 can be trapped in themicro-pore space as droplets surrounded by water.At this small scale, the contribution of the interfaceenergyto the total energyis consequential, and thuscomes into play. Various phase field models basedon free energies are often used to study the dynam-i...

arXiv: Fluid Dynamics, 2014

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle. The dynamics of the fluids satisfy the conservation laws of mass, momentum, angular momentum, and energy, and obey the second law of thermodynamics. By Noether’s theorem, these conservation laws are associated with the corresponding symmetries. On the other hand, the equation for entropy gives a nonholonomic constraint. Then Lagrangians and this nonholonomic constraint of the fluids satisfy these symmetries. The dynamics of fluid are given as a weak solution, minimizing an action subject to this constraint. For the existence of the weak solution, all the surface terms appearing in the variational calculus have to vanish with the aid of the nonholonomic constraint. In this study, we show that the equation for entropy is determined to be consist to “the second law of thermodynamics”, “the symmetries”, and “the necessary condition of the existence of the weak so...

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

Progress of Theoretical Physics, 2010

Progress of Theoretical Physics, 2012

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Nihon Butsuri Gakkaishi, 2017

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature... more We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

We propose equations governing the dissolution in inhomogeneous temperature field in terms of the... more We propose equations governing the dissolution in inhomogeneous temperature field in terms of the variational principle. The derived equations clarify that the interface energy between solute and solvent has a significant effect on the process of the dissolution. The interface energy restrains the dissolution, and the moving interface involves the heat of dissolution.

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle.

We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint... more We propose a formalization for dissipative fluids in inhomogeneous temperature from the viewpoint of a variational principle. The dynamics of the fluids satisfy the conservation laws of mass, momentum, angular momentum, and energy, and obey the second law of thermodynamics. By Noether's theorem, these conservation laws are associated with the corresponding symmetries. On the other hand, the equation for entropy gives a nonholonomic constraint. Then Lagrangians and this nonholonomic constraint of the fluids satisfy these symmetries. The dynamics of fluid are given as a weak solution, minimizing an action subject to this constraint. For the existence of the weak solution, all the surface terms appearing in the variational calculus have to vanish with the aid of the nonholonomic constraint. In this study, we show that the equation for entropy is determined to be consist to "the second law of thermodynamics", "the symmetries", and "the necessary condition of the existence of the weak solution". Our method gives a general scheme to derive the equation of motion for fluids in inhomogeneous temperature, and gives an explanation of some nontrivial thermal effects on the rotation of liquid crystal, vaporization of a one component fluid, and dissolution of a two component fluid.

In the variational principle leading to the Euler equation for a perfect fluid, we can use the me... more In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Progress of Theoretical Physics, 2010

Equations for a perfect fluid can be obtained by means of the variational principle both in the L... more Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in the latter description. We give a simple explanation for these fields; they are introduced to fix both ends of a pathline in the variational calculus. This restriction is imposed in the former description, and should be imposed in the latter description. It is also shown that we can derive a canonical Hamiltonian formulation for a perfect fluid by regarding the velocity field as the input in the framework of control theory.