The terminal velocity of a liquid droplet settling in a sulfactant solution has been studied for the non-linear adsorption Langmuir frameworks accounting for monolayer saturation and non-ideal surfactant interactions....The terminal velocity of a liquid droplet settling in a sulfactant solution has been studied for the non-linear adsorption Langmuir frameworks accounting for monolayer saturation and non-ideal surfactant interactions. Most prior research uses a linear adsorption model which cannot capture these effects, The Maragoni migration of a liquid drop settling through a surfactant solution is examined by using Langmuir framework. The solution concentration Ceq is assumed large enough for the surfactant mass transfer to be adsorption-controlled. Langmuir model generates non-linear Marangoni stresses which diverge in the limit of approaching ∝, strongly retarding U'.展开更多
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the deri...With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.展开更多
Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based...Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.展开更多
Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the a...Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.展开更多
We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe t...We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.展开更多
We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles inst...We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.展开更多
Eruptive fires are one of the main causes of human losses in forest fire fighting. The sudden change in fire behaviour due to a fire eruption is extremely dangerous for fire-fighters because it is unpredictable. Very ...Eruptive fires are one of the main causes of human losses in forest fire fighting. The sudden change in fire behaviour due to a fire eruption is extremely dangerous for fire-fighters because it is unpredictable. Very little literature is available to support either modelling or occurrence prediction for this phenomenon. In this study, an unsteady physical model of fire spread is detailed, which describes the initiation and development of eruptive fires with an induced wind sub-model. The latter phenomenon is proposed as the mainspring of fire eruptions. Induced wind is proportional to the rate of spread and the rate of spread is in a non-linear relationship with induced wind. This feedback can converge or diverge depending on the conditions. The model allows both explaining why an eruption can occur and predicting explicitly its occurrence according to meteorological conditions, topographic parameters, fuel bed properties and fire front width. The model is tested by comparing its results to a set of experiments carried out at laboratory scale and during an outdoor wildfire, the Kornati accident.展开更多
Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is p...Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.展开更多
The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find inter...The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.展开更多
In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Fie...In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.展开更多
The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,th...The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.展开更多
All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light ...All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically,from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L × SU(2)_R× U(1)_(B-L). Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV–2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.展开更多
文摘The terminal velocity of a liquid droplet settling in a sulfactant solution has been studied for the non-linear adsorption Langmuir frameworks accounting for monolayer saturation and non-ideal surfactant interactions. Most prior research uses a linear adsorption model which cannot capture these effects, The Maragoni migration of a liquid drop settling through a surfactant solution is examined by using Langmuir framework. The solution concentration Ceq is assumed large enough for the surfactant mass transfer to be adsorption-controlled. Langmuir model generates non-linear Marangoni stresses which diverge in the limit of approaching ∝, strongly retarding U'.
文摘With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
基金The project supported by the Natural Science Foundation of Inner Mongolia under Grant No. 200408020113 and National Natural Science Foundation of China under Grant No. 40564001
文摘Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.
文摘Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.
基金Supported by National Natural Science Foundation of China under Grant No.60821002/F02
文摘We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
基金supported by National Natural Science Foundation of China under Grant No.60674062the Middle-Aged and Young Scientists Research Incentive Fund of Shandong Province under Grant No.2007BS01013
文摘We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.
文摘Eruptive fires are one of the main causes of human losses in forest fire fighting. The sudden change in fire behaviour due to a fire eruption is extremely dangerous for fire-fighters because it is unpredictable. Very little literature is available to support either modelling or occurrence prediction for this phenomenon. In this study, an unsteady physical model of fire spread is detailed, which describes the initiation and development of eruptive fires with an induced wind sub-model. The latter phenomenon is proposed as the mainspring of fire eruptions. Induced wind is proportional to the rate of spread and the rate of spread is in a non-linear relationship with induced wind. This feedback can converge or diverge depending on the conditions. The model allows both explaining why an eruption can occur and predicting explicitly its occurrence according to meteorological conditions, topographic parameters, fuel bed properties and fire front width. The model is tested by comparing its results to a set of experiments carried out at laboratory scale and during an outdoor wildfire, the Kornati accident.
基金Supported by the National Natural Science Foundation of China under Grant No.10735030 the National Basic Research Programs of China (973 Programs) under Grant Nos.2007CB814800 and 2005CB422301the PCSIRT (IRT0734)
文摘Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.
基金Supported by the National Natural Science Foundations of China under Grant No.11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.
文摘In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.
文摘The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
基金KITPC financial support during the completion of this work
文摘All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically,from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L × SU(2)_R× U(1)_(B-L). Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV–2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.
