Developing a novel drop counter by introducing the Internet of Things concept has been vigorously conducted in recent years. Understanding the newly introduced drop counter’s flow rate control accuracy and flow rate ...Developing a novel drop counter by introducing the Internet of Things concept has been vigorously conducted in recent years. Understanding the newly introduced drop counter’s flow rate control accuracy and flow rate count feature is essential for improving safety in infusion management. This study aimed to verify if the new drop counters could secure accurate flow rate and drip count by conducting actual flow rate measurements using gravimetry and functional evaluation. A drop counter was attached to each drip chamber of the infusion set, and an IV drip was conducted at the 100 ml/h flow rate. The weight of discharged physiological saline was measured to plot trumpet curves. Next, three different types of drop counters were evaluated to determine if they maintained drip count accuracy according to the changes in their position angles. The flow rate errors in all conditions indicated trumpet-like curves, exhibiting an overall error range within ±10% in all observation windows. Although every drop counter successfully detected and measured dripping, it was challenging in some counters to detect dripping when the drip chamber was tilted. In comparing adult and pediatric IV sets, the adult IV set was found to be less likely to detect dripping in the angled position. No significant differences in results were confirmed between high and low flow rates, suggesting that the drop count function would not be affected by the flow rate in the ranges of typical infusion practices. Doppler sensors have a wide range of measurements and high sensitivity;the dripping was detected successfully even when the drip chamber was tilted, probably due to the advantages of these sensors. In contrast, miscounts occurred in those equipped with infrared sensors, which could not detect light intensity changes in tilted positions. Understanding the tendencies in flow rate errors in infusion can be valuable information for infusion management.展开更多
A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other fi...A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.展开更多
A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a duali...A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a dualism-based analysis that explains the origin of charge at the fermion scale in a primordial field theory of quantum gravity.展开更多
In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of...In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity.Four key parameters,including the flow velocity,the mass ratio,the gravity parameter,and the inclination angle between the pipe length and the gravity direction,are considered to affect the static and dynamic behaviors of the soft pipe.The stability analyses show that,provided that the inclination angle is not equal to π,the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value.As the inclination angle is equal to π,the pipe experiences,in turn,buckling instability,regaining stability,and flutter instability with the increase in the flow velocity.Interestingly,the stability of the pipe can be either enhanced or weakened by varying the gravity parameter,mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis,it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations.Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.展开更多
The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the ...The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.展开更多
Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper.A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived.A dimensionless...Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper.A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived.A dimensionless memory(time)number θ is introduced.The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0.The complex dispersion equation is numerically solved to investigate the dispersion relation.The influences of θ and water depth on the dispersion characteristics and wave decay are discussed.It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.展开更多
Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures ...Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and 'action-angle' varia-bles are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.展开更多
We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Pl...We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Planck length without requiring knowledge of either G or the Planck constant. This experiment is simple to perform and cost-effective, making it not only of interest to researchers studying gravity but also suitable for low-budget educational settings. Despite its simplicity, this has never been demonstrated to be possible before, and it is achievable due to new theoretical insights into gravity and its connection to quantum gravity and the Planck scale. This provides new insights into fluid mechanics and the Planck scale. We are also exploring initial concepts related to what we are calling “Planck fluid”, which could potentially play a central role in quantum gravity and quantum fluid mechanics.展开更多
In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are obtained.Firstly,using the Lie symmetries,symmetry reductions are performed for considered ve...In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are obtained.Firstly,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent variables.Then,corresponding to each reduction,exact solutions are obtained.Killing vectors lead to different conserved quantities.Therefore,we figure out the Killing vector fields corresponding to all derived solutions.The derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector fields.Conservation of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.展开更多
Reservoirs can be developed in the sediment gravity flows.However,high quality reservoirs are found widespread in sediment gravity flows of Gangzhong area,Huanghua depression,Bohai Bay Basin,East China.Characteristics...Reservoirs can be developed in the sediment gravity flows.However,high quality reservoirs are found widespread in sediment gravity flows of Gangzhong area,Huanghua depression,Bohai Bay Basin,East China.Characteristics and formation of these reservoirs are key problems to be solved.Through comprehensive analysis of thin section petrography,scanning electron microscopy and X-ray diffraction,two distinct rules were obtained.1) These high quality reservoirs have apparent characteristics:lithology consists mainly of medium-fine grained sands; moderately-well sorted and rounded; intergranular pores dominating >70% of the entire pores,surface per unit pore volume reaches 15%; average porosity is 21% and average permeability is 55×10-3 μm2.2) Types of sedimentary microfacies and dissolution strongly control on the formation of high quality reservoirs.Main channels and sandy braided bars have the best reservoir properties.Because that sediments are mainly medium-fine grained sands in high-energy environments.The favorable primary porosity and permeability may promote calcite cementation and help to produce more secondary pores.Besides,at the depth of 2500-3200 m,basically matching threshold of oil generation,organic acid expelled when organic matter became mature,and H+ released during clay mineral transformation.These both result in the dissolution of calcite cements and create large volume pores,then physical properties improve correspondingly.Moreover,deep hydrothermal fluid intrusion may also have impacts on the development of secondary pores.展开更多
By the Volume of Fluid (VOF) multiphase flow model two-dimensional gravity currents with three phases including air are numerically simulated in this article. The necessity of consideration of turbulence effect for hi...By the Volume of Fluid (VOF) multiphase flow model two-dimensional gravity currents with three phases including air are numerically simulated in this article. The necessity of consideration of turbulence effect for high Reynolds numbers is demonstrated quantitatively by LES (the Large Eddy Simulation) turbulence model. The gravity currents are simulated for h not equal H as well as h = H, where h is the depth of the gravity current before the release and H is the depth of the intruded fluid. Uprising of swell occurs when a current flows horizontally into another lighter one for h not equal H. The problems under what condition the uprising of swell occurs and how long it takes are considered in this article. All the simulated results are in reasonable agreement with the experimental results available.展开更多
Lock-release gravity currents with a viscous self-similar regime are simulated by use of the renormalization group (RNG) k-ε model for Reynolds-stress closure. Besides the turbulent regime with initially a slumping p...Lock-release gravity currents with a viscous self-similar regime are simulated by use of the renormalization group (RNG) k-ε model for Reynolds-stress closure. Besides the turbulent regime with initially a slumping phase of a constant current front speed and later an inviscid self-similar phase of front speed decreasing as t -1/3 (where t is the time measured from release), the viscous self-similar regime is satisfactorily reproduced with front speed decreasing as t -4/5, consistent with well known experimental observations.展开更多
By means of numerical simulation. the in fluence of gravity on fluid flow,patterns has been simulated.The result shows that with the increase of inclined angle,the velocity of fluid flow decreases and the isotherms be...By means of numerical simulation. the in fluence of gravity on fluid flow,patterns has been simulated.The result shows that with the increase of inclined angle,the velocity of fluid flow decreases and the isotherms become flatter,which suppresses the evolution of channel segregation.展开更多
We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the unique...We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from 3 + 1 dimensions to arbitrary n + 1 Ds and find that the n + 1 ≥ 5D charged AdS domain walls are unstable against electric perturbations.展开更多
In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energ...In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energy-momentum tensor and μ is a constant. Two cosmological models are constructed using the power law expansion and hybrid law cosmology in Bianchi type I universe, where the matter field is considered to be a perfect fluid. It is found that in both the cases the anisotropic behavior is in agreement with the observational results. The state finder diagnostic pair and energy conditions are also calculated and analyzed.展开更多
We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models ar...We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models are constructed and analyzed in detail. We found that the state parameter in both the models increases to a higher negative range in an early epoch of the phantom domain and it goes to the positive domain at a late phase of the evolution. The effective cosmological constant remains in a positive domain for both models, which is a good sign of accelerating expansion of the universe.展开更多
Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures...Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures which are preserved. We apply the resulting construction to convert the BTZ black hole metric to ITQG framework. We then modify the BTZ black hole in order to investigate the existence of the P-V criticality in ITQG theory.展开更多
文摘Developing a novel drop counter by introducing the Internet of Things concept has been vigorously conducted in recent years. Understanding the newly introduced drop counter’s flow rate control accuracy and flow rate count feature is essential for improving safety in infusion management. This study aimed to verify if the new drop counters could secure accurate flow rate and drip count by conducting actual flow rate measurements using gravimetry and functional evaluation. A drop counter was attached to each drip chamber of the infusion set, and an IV drip was conducted at the 100 ml/h flow rate. The weight of discharged physiological saline was measured to plot trumpet curves. Next, three different types of drop counters were evaluated to determine if they maintained drip count accuracy according to the changes in their position angles. The flow rate errors in all conditions indicated trumpet-like curves, exhibiting an overall error range within ±10% in all observation windows. Although every drop counter successfully detected and measured dripping, it was challenging in some counters to detect dripping when the drip chamber was tilted. In comparing adult and pediatric IV sets, the adult IV set was found to be less likely to detect dripping in the angled position. No significant differences in results were confirmed between high and low flow rates, suggesting that the drop count function would not be affected by the flow rate in the ranges of typical infusion practices. Doppler sensors have a wide range of measurements and high sensitivity;the dripping was detected successfully even when the drip chamber was tilted, probably due to the advantages of these sensors. In contrast, miscounts occurred in those equipped with infrared sensors, which could not detect light intensity changes in tilted positions. Understanding the tendencies in flow rate errors in infusion can be valuable information for infusion management.
文摘A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.
文摘A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a dualism-based analysis that explains the origin of charge at the fermion scale in a primordial field theory of quantum gravity.
基金Project supported by the National Natural Science Foundation of China(Nos.11672115,11622216,and 11972167)。
文摘In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity.Four key parameters,including the flow velocity,the mass ratio,the gravity parameter,and the inclination angle between the pipe length and the gravity direction,are considered to affect the static and dynamic behaviors of the soft pipe.The stability analyses show that,provided that the inclination angle is not equal to π,the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value.As the inclination angle is equal to π,the pipe experiences,in turn,buckling instability,regaining stability,and flutter instability with the increase in the flow velocity.Interestingly,the stability of the pipe can be either enhanced or weakened by varying the gravity parameter,mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis,it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations.Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.
文摘The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.
基金The project supported by the National Natural Science Foundation of China(50279029)
文摘Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper.A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived.A dimensionless memory(time)number θ is introduced.The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0.The complex dispersion equation is numerically solved to investigate the dispersion relation.The influences of θ and water depth on the dispersion characteristics and wave decay are discussed.It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.
基金Project supported by NSFC for Youtb(No.B909920106)
文摘Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and 'action-angle' varia-bles are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.
文摘We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Planck length without requiring knowledge of either G or the Planck constant. This experiment is simple to perform and cost-effective, making it not only of interest to researchers studying gravity but also suitable for low-budget educational settings. Despite its simplicity, this has never been demonstrated to be possible before, and it is achievable due to new theoretical insights into gravity and its connection to quantum gravity and the Planck scale. This provides new insights into fluid mechanics and the Planck scale. We are also exploring initial concepts related to what we are calling “Planck fluid”, which could potentially play a central role in quantum gravity and quantum fluid mechanics.
基金UGC for providing financial support in the form of the JRF fellowship via letter NTA Ref.No.:201610006334the financial support provided under the scheme‘Fund for Improvement of S&T Infrastructure(FIST)’of the Department of Science&Technology(DST),Government of India via letter No.SR/FST/MS-I/2021/104 to the Department of Mathematics and Statistics,Central University of Punjab。
文摘In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are obtained.Firstly,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent variables.Then,corresponding to each reduction,exact solutions are obtained.Killing vectors lead to different conserved quantities.Therefore,we figure out the Killing vector fields corresponding to all derived solutions.The derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector fields.Conservation of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.
基金Project(2006CB202300)supported by the National Basic Research Program of China
文摘Reservoirs can be developed in the sediment gravity flows.However,high quality reservoirs are found widespread in sediment gravity flows of Gangzhong area,Huanghua depression,Bohai Bay Basin,East China.Characteristics and formation of these reservoirs are key problems to be solved.Through comprehensive analysis of thin section petrography,scanning electron microscopy and X-ray diffraction,two distinct rules were obtained.1) These high quality reservoirs have apparent characteristics:lithology consists mainly of medium-fine grained sands; moderately-well sorted and rounded; intergranular pores dominating >70% of the entire pores,surface per unit pore volume reaches 15%; average porosity is 21% and average permeability is 55×10-3 μm2.2) Types of sedimentary microfacies and dissolution strongly control on the formation of high quality reservoirs.Main channels and sandy braided bars have the best reservoir properties.Because that sediments are mainly medium-fine grained sands in high-energy environments.The favorable primary porosity and permeability may promote calcite cementation and help to produce more secondary pores.Besides,at the depth of 2500-3200 m,basically matching threshold of oil generation,organic acid expelled when organic matter became mature,and H+ released during clay mineral transformation.These both result in the dissolution of calcite cements and create large volume pores,then physical properties improve correspondingly.Moreover,deep hydrothermal fluid intrusion may also have impacts on the development of secondary pores.
基金This paper was supported by the National Natural Science Foundation of China (Grant No.19972061)
文摘By the Volume of Fluid (VOF) multiphase flow model two-dimensional gravity currents with three phases including air are numerically simulated in this article. The necessity of consideration of turbulence effect for high Reynolds numbers is demonstrated quantitatively by LES (the Large Eddy Simulation) turbulence model. The gravity currents are simulated for h not equal H as well as h = H, where h is the depth of the gravity current before the release and H is the depth of the intruded fluid. Uprising of swell occurs when a current flows horizontally into another lighter one for h not equal H. The problems under what condition the uprising of swell occurs and how long it takes are considered in this article. All the simulated results are in reasonable agreement with the experimental results available.
文摘Lock-release gravity currents with a viscous self-similar regime are simulated by use of the renormalization group (RNG) k-ε model for Reynolds-stress closure. Besides the turbulent regime with initially a slumping phase of a constant current front speed and later an inviscid self-similar phase of front speed decreasing as t -1/3 (where t is the time measured from release), the viscous self-similar regime is satisfactorily reproduced with front speed decreasing as t -4/5, consistent with well known experimental observations.
文摘By means of numerical simulation. the in fluence of gravity on fluid flow,patterns has been simulated.The result shows that with the increase of inclined angle,the velocity of fluid flow decreases and the isotherms become flatter,which suppresses the evolution of channel segregation.
文摘We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from 3 + 1 dimensions to arbitrary n + 1 Ds and find that the n + 1 ≥ 5D charged AdS domain walls are unstable against electric perturbations.
文摘In this paper, the dynamical behavior of an anisotropic universe in an extended gravity e.g. the f (R,T ) theory of gravity is studied. We use f (R,T ) = R + 2μT , where R is the Ricci scalar, T is the trace of energy-momentum tensor and μ is a constant. Two cosmological models are constructed using the power law expansion and hybrid law cosmology in Bianchi type I universe, where the matter field is considered to be a perfect fluid. It is found that in both the cases the anisotropic behavior is in agreement with the observational results. The state finder diagnostic pair and energy conditions are also calculated and analyzed.
文摘We report a viable exponential gravity model for the accelerated expansion of the universe in Bianchi VI<sub>h</sub> space-time. By considering the estimated physical parameters, the cosmological models are constructed and analyzed in detail. We found that the state parameter in both the models increases to a higher negative range in an early epoch of the phantom domain and it goes to the positive domain at a late phase of the evolution. The effective cosmological constant remains in a positive domain for both models, which is a good sign of accelerating expansion of the universe.
文摘Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures which are preserved. We apply the resulting construction to convert the BTZ black hole metric to ITQG framework. We then modify the BTZ black hole in order to investigate the existence of the P-V criticality in ITQG theory.