TAILIEUCHUNG - Normal mode vs parabolic equation and their application in Tonkin Gulf

In this paper, author investigates NM and PE in term of their mathematical approach as well as their computation. Further, Tonkin Gulf has been modeled and simulated using both of NM and PE. The simulation results show that there are the agreement and the reliability between both methodologies. | Normal mode vs parabolic equation and their application in Tonkin Gulf P-ISSN 1859-3585 E-ISSN 2615-9615 SCIENCE - TECHNOLOGY NORMAL MODE vs PARABOLIC EQUATION AND THEIR APPLICATION IN TONKIN GULF MODE CHUẨN SO VỚI PHƯƠNG TRÌNH PARABOLIC VÀ ÁP DỤNG VÀO VỊNH BẮC BỘ Tran Cao Quyen to an eigenfunction (mode shape) and an eigenvalue ABSTRACT (horizontal propagation constant). Normal Mode (NM) and Parabolic Equation (PE) have been used widely by Third, the PE method is introduced firstly by Tappert [5] Underwater Acoustic Community due to their effectiveness. In this paper, author investigates NM and PE in term of their mathematical approach as well as their and is considered the modern method since it applied for computation. Further, Tonkin Gulf has been modeled and simulated using both the medium which has layers separated unclearly [5-8]. The of NM and PE. The simulation results show that there are the agreement and the advantages of parabolic method consists of using a source reliability between both methodologies. with one-way propagation, applying for range dependence, as well as performing in the medium which is Keywords: SONAR, Parabolic Equation, Normal Mode, Tonkin Gulf. not required exactly layered separation. TÓM TẮT In this paper we investigate NM and PE in term of their Phương pháp Mode chuẩn và phương trình Parabolic được dùng rộng rãi mathematical approach as well as their computation. trong cộng đồng thủy âm vì sự hiệu quả của chúng. Trong bài báo này, tác giả Besides, Tonkin Gulf has been modeled and simulated nghiên cứu mode chuẩn và phương trình Parabolic ở khía cạnh toán học và tốc độ using not only NM but also PE. The obtained results show tính toán. Hơn nữa, Vịnh Bắc Bộ được mô hình hóa và mô phỏng dùng cả mode that when we divided the grid small enough (the depth, chuẩn và phương trình Parabolic. Các kết quả mô phỏng cho thấy có sự đồng z , the range, r (5 10) z , the parabolic .

• Địa Lý
• Parabolic equation
• Normal mode
• Tonkin Gulf
• Mathematical approach
• Ocean acoustic computation
• Prabolic equation
• Bi spaces
• Quasilinear parabolic equation
• Long time behavior of solutions
• Faedo Galerkin approximation
• Semilinear parabolic equation
• Blow up
• Numerical blow up time
• Variable reaction
• Dirichlet boundary
• Four step implicit
• Almost optimal
• Nonlinear parabolic equation
• Elliptic projection operators
• Partial differential equation
• Finite element method
• Quenching behavior
• Non linear source
• Nonlinear source
• Continuity of the quenching time
• Adaptive method on the quenching time
• Neumann conditions
• Exhibit a solution
• Bài viết nghiên cứu khoa học
• Global attractor
• Grushin operator
• Gronwall inequality
• Gamma equation
• Maximum principle
• Monotone finite difference scheme
• Non uniform grid
• Quasi linear parabolic equation
• Scientific computing
• Two side estimates
• parabolic Ginzburg Landau
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Quasilinear degenerate parabolic equation
• Weighted p Laplacian operator
• Weak solution
• Compactness method
• Monotonicity method
• Hall effect
• Quantum kinetic equation
• Parabolic quantum wells
• Electron phonon interaction
• Mathematical and physical
• Cauchy Dirichlet problem
• Nonsmooth domains
• Conical points
• The regularity
• Absorption coefficient
• Asymmetric semi parabolic quantum wells
• Electron phonon scattering
• Electromagnetic wave
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• báo cáo khoa học
• Optimal control problem
• Finite difference method
• Inverse problem
• Linear parabolic equations
• Speed of convergence
• Backward heat problem
• Modified quasi Boundary value method
• Polar coordinates
• Ill posed problem
• Mixed Neumann Robin Cauchy problem
• Discontinuous coefficient
• Bounded solution
• Robin boundary condition