Objective Model Selection in Physics: Exploring the Finite Information Quantity Approach

Traditional methods for selecting models in experimental data analysis are susceptible to researcher bias, hindering exploration of alternative explanations and potentially leading to overfitting. The Finite Information Quantity (FIQ) approach offers a novel solution by acknowledging the inherent limitations in information processing capacity of physical systems. This framework facilitates the development of objective criteria for model selection (comparative uncertainty) and paves the way for a more comprehensive understanding of phenomena through exploring diverse explanations. This work presents a detailed comparison of the FIQ approach with ten established model selection methods, highlighting the advantages and limitations of each. We demonstrate the potential of FIQ to enhance the objectivity and robustness of scientific inquiry through three practical examples: selecting appropriate models for measuring fundamental constants, sound velocity, and underwater electrical discharges. Further research is warranted to explore the full applicability of FIQ across various scientific disciplines.

Tribological Performance of Different Concentrations of Al_(2)O_(3)Nanofluids on Minimum Quantity Lubrication Milling

Nanofluid minimum quantity lubrication(NMQL)is a green processing technology.Cottonseed oil is suitable as base oil because of excellent lubrication performance,low freezing temperature,and high yield.Al_(2)O_(3)nanoparticles improve not only the heat transfer capacity but also the lubrication performance.The physical and chemical proper-ties of nanofluid change when Al_(2)O_(3)nanoparticles are added.However,the effects of the concentration of nanofluid on lubrication performance remain unknown.Furthermore,the mechanisms of interaction between Al_(2)O_(3)nanoparti-cles and cottonseed oil are unclear.In this research,nanofluid is prepared by adding different mass concentrations of Al_(2)O_(3)nanoparticles(0,0.2%,0.5%,1%,1.5%,and 2%wt)to cottonseed oil during minimum quantity lubrication(MQL)milling 45 steel.The tribological properties of nanofluid with different concentrations at the tool/workpiece interface are studied through macro-evaluation parameters(milling force,specific energy)and micro-evaluation parameters(surface roughness,micro morphology,contact angle).The result show that the specific energy is at the minimum(114 J/mm^(3)),and the roughness value is the lowest(1.63μm)when the concentration is 0.5 wt%.The surfaces of the chip and workpiece are the smoothest,and the contact angle is the lowest,indicating that the tribological proper-ties are the best under 0.5 wt%.This research investigates the intercoupling mechanisms of Al_(2)O_(3)nanoparticles and cottonseed base oil,and acquires the optimal Al_(2)O_(3)nanofluid concentration to receive satisfactory tribological properties.

Tribological Mechanism of Graphene and Ionic Liquid Mixed Fluid on Grinding Interface under Nanofluid Minimum Quantity Lubrication

Graphene has superhigh thermal conductivity up to 5000 W/(m·K),extremely thin thickness,superhigh mechanical strength and nano-lamellar structure with low interlayer shear strength,making it possess great potential in mini-mum quantity lubrication(MQL)grinding.Meanwhile,ionic liquids(ILs)have higher thermal conductivity and better thermal stability than vegetable oils,which are frequently used as MQL grinding fluids.And ILs have extremely low vapor pressure,thereby avoiding film boiling in grinding.These excellent properties make ILs also have immense potential in MQL grinding.However,the grinding performance of graphene and ionic liquid mixed fluid under nano-fluid minimum quantity lubrication(NMQL),and its tribological mechanism on abrasive grain/workpiece grinding interface,are still unclear.This research firstly evaluates the grinding performance of graphene and ionic liquid mixed nanofluids(graphene/IL nanofluids)under NMQL experimentally.The evaluation shows that graphene/IL nanofluids can further strengthen both the cooling and lubricating performances compared with MQL grinding using ILs only.The specific grinding energy and grinding force ratio can be reduced by over 40%at grinding depth of 10μm.Work-piece machined surface roughness can be decreased by over 10%,and grinding temperature can be lowered over 50℃at grinding depth of 30μm.Aiming at the unclear tribological mechanism of graphene/IL nanofluids,molecular dynamics simulations for abrasive grain/workpiece grinding interface are performed to explore the formation mechanism of physical adsorption film.The simulations show that the grinding interface is in a boundary lubrication state.IL molecules absorb in groove-like fractures on grain wear flat face to form boundary lubrication film,and graphene nanosheets can enter into the grinding interface to further decrease the contact area between abrasive grain and workpiece.Compared with MQL grinding,the average tangential grinding force of graphene/IL nanofluids can decrease up to 10.8%.The interlayer shear effect and low interlayer shear strength of graphene nanosheets are the principal causes of enhanced lubricating performance on the grinding interface.EDS and XPS analyses are further carried out to explore the formation mechanism of chemical reaction film.The analyses show that IL base fluid happens chemical reactions with workpiece material,producing FeF_(2),CrF_(3),and BN.The fresh machined surface of workpiece is oxidized by air,producing NiO,Cr_(2)O_(3) and Fe_(2)O_(3).The chemical reaction film is constituted by fluorides,nitrides and oxides together.The combined action of physical adsorption film and chemical reaction film make graphene/IL nano-fluids obtain excellent grinding performance.

Qualia Role-Based Quantity Relation Extraction for Solving Algebra Story Problems

A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translate problem texts into math expressions,which lack quantity relation acquisition in sophisticated scenarios.To address the problem,the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects.Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems.Experimental result shows that the proposedmethod achieved an average accuracy of 82.2%on quantity relation extraction compared to 74.5%of baseline method.Another prompt learning result shows a 5%increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.

Symmetry and Hojman Conserved Quantity of Tznoff Equations for Unilateral Holonomic System

Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.

The estimate of sea ice resources quantity in the Bohai Sea based on NOAA/AVHRR data

The research on sea ice resources is the academic base of sea ice exploitation in the Bohai Sea. According to the ice-water spectrum differences and the correlation between ice thickness and albedo, this paper comes up with a sea ice thickness inversion model based on the NOAA/AVHRR data. And then a sea ice resources quantity （SIQ） time series of Bohai Sea is established from 1987 to 2009. The results indicate that the average error of inversion sea ice thickness is below 30%. The maximum sea ice resources quantity is about 6×109 m3 and the minimum is 1.3×109 m3. And a preliminary analysis has been made on the errors of the estimate of sea ice resources quantity （SIQ）.

Effect of sensor quantity on measurement accuracy of log inner defects by using stress wave

Wood nondestructive testing （NDT） is one of the high efficient methods in utilizing wood. This paper explained the principle of log defect testing by using stress wave, and analyzed the effects of sensor quantity on defect testing results by using stress wave in terms of image fitting degree and error rate. The results showed that for logs with diameter ranging from 20 to 40 cm, at least 12 sensors were needed to meet the requirement which ensure a high testing accuracy of roughly 90% of fitness with 0.1 of error rate. And 10 sensors were recommended to judge the possible locations of defects and 6 sensors were sufficient to decide whether there were defects or not.

A symmetry and a conserved quantity for the Birkhoff system

A symmetry and a conserved quantity of the Birkhoff system are studied. The symmetry is called the Birkhoff symmetry. Its definition and criterion are given in this paper. A conserved quantity can be deduced by using the symmetry. An example is given to illustrate the application of the result.

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Improved grey prediction model based on exponential grey action quantity

With the passage of time, it has become important to investigate new methods for updating data to better fit the trends of the grey prediction model. The traditional GM（1,1） usually sets the grey action quantity as a constant. Therefore, it cannot effectively fit the dynamic characteristics of the sequence, which results in the grey model having a low precision. The linear grey action quantity model cannot represent the index change law. This paper presents a grey action quantity model, the exponential optimization grey model（EOGM（1,1））, based on the exponential type of grey action quantity; it is constructed based on the exponential characteristics of the grey prediction model. The model can fully reflect the exponential characteristics of the simulation series with time. The exponential sequence has a higher fitting accuracy. The optimized result is verified using a numerical example for the fluctuating sequence and a case study for the index of the tertiary industry＇s GDP. The results show that the model improves the precision of the grey forecasting model and reduces the prediction error.

A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

A new type of conserved quantity of Lie symmetry for the Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.

Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.

A new type of conserved quantity of Mei symmetry for Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are dis-cussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.

Structure equation and Mei conserved quantity for Mei symmetry of Appell equation

This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.

Lie symmetry and conserved quantity of a system of first-order differential equations

This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.

Electrostatic atomization minimum quantity lubrication machining:from mechanism to application

Metal cutting fluids(MCFs)under flood conditions do not meet the urgent needs of reducing carbon emission.Biolubricant-based minimum quantity lubrication(MQL)is an effective alternative to flood lubrication.However,pneumatic atomization MQL has poor atomization properties,which is detrimental to occupational health.Therefore,electrostatic atomization MQL requires preliminary exploratory studies.However,systematic reviews are lacking in terms of capturing the current research status and development direction of this technology.This study aims to provide a comprehensive review and critical assessment of the existing understanding of electrostatic atomization MQL.This research can be used by scientists to gain insights into the action mechanism,theoretical basis,machining performance,and development direction of this technology.First,the critical equipment,eco-friendly atomization media(biolubricants),and empowering mechanisms of electrostatic atomization MQL are presented.Second,the advanced lubrication and heat transfer mechanisms of biolubricants are revealed by quantitatively comparing MQL with MCF-based wet machining.Third,the distinctive wetting and infiltration mechanisms of electrostatic atomization MQL,combined with its unique empowering mechanism and atomization method,are compared with those of pneumatic atomization MQL.Previous experiments have shown that electrostatic atomization MQL can reduce tool wear by 42.4%in metal cutting and improve the machined surface Ra by 47%compared with pneumatic atomization MQL.Finally,future development directions,including the improvement of the coordination parameters and equipment integration aspects,are proposed.

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.