Chapter 1
Introduction

Many of the important technological problems confronting the Navy cannot be analyzed using the linear techniques that have dominated engineering development over the past hundred years. The fundamental assumption of linear methods, that response is proportional to stimulus, fails utterly in far-from-equilibrium systems such as turbulent wakes, rocket and jet engine combustion, or detonating explosives, in which a small stimulus can produce an enormous response. Similarly, the linear assumption that a large system is simply the sum of its individual parts is invalid for the complex systems found in automated defense technologies where subsystems interact strongly and the behavior of the whole cannot be anticipated or controlled by linear algorithms.

For both far-from-equilibrium and complex systems, the emerging concepts of nonlinear science are essential. Nonlinear science (NLS) represents, to some extent, a reorganization of the traditional categories of analysis. These categories are connected across, rather than along, the traditional lines between the physical sciences. Further, NLS relies on some qualitatively distinct methods that have the potential to make significant contributions to the next generation of engineering analysis.

The greatest potential for NLS is the creation of new technologies by introducing fundamentally different capabilities and by integrating ideas across the normal disciplinary lines. In this regard, the recent nonlinear revolution has been compared to the early twentieth century quantum revolution. Quantum mechanics did not change the classical world. It did not reduce friction or make engines run more efficiently. Instead, it provided qualitatively new tools for use in the microscopic world. Similarly, nonlinear science will not change the linear world or undo the successes of linear approaches. However, it will provide the essential techniques for understanding, manipulating, and controlling complex systems, processes occurring far from equilibrium, and other important phenomena that underlie the naval technologies of the future.

The central thesis of this report is that the nurturing of a coordinated experimental, computational, and theoretical effort in nonlinear science at the Naval Research Laboratory (NRL) is crucial to emerging Navy technologies. The elements of nonlinear science permeate naval needs from antisubmarine warfare to targeting for strategic defense.

In the remainder of the report, this thesis is developed and supported in some detail. Chapter 2 provides relevant administrative and scientific background information on nonlinear science. Chapter 3 provides several detailed examples of successful transitions from basic concepts of nonlinear science to important technological applications.

In Chapter 4, the heart of this report, six broad areas are examined in which Navy needs, NRL capabilities, and nonlinear science opportunities coincide. In each of these six general areas, specific problems are identified whose solutions will provide critical and in some cases rapid progress on significant naval needs.

Recommendations are discussed in Chapter 5. It is argued that the continued support of a core NLS group is necessary to maintain the excellent research effort in nonlinear science and to provide technical support for, and stimulate interactions among, the many science and engineering efforts at NRL in which NLS is essential for genuine progress.



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Chapter 1 Introduction Many of the important technological problems confronting the Navy cannot be analyzed using the linear techniques that have dominated engineering development over the past hundred years. The fundamental assumption of linear methods, that response is proportional to stimulus, fails utterly in far-from-equilibrium systems such as turbulent wakes, rocket and jet engine combustion, or detonating explosives, in which a small stimulus can produce an enormous response. Similarly, the linear assumption that a large system is simply the sum of its individual parts is invalid for the complex systems found in automated defense technologies where subsystems interact strongly and the behavior of the whole cannot be anticipated or controlled by linear algorithms. For both far-from-equilibrium and complex systems, the emerging concepts of nonlinear science are essential. Nonlinear science (NLS) represents, to some extent, a reorganization of the traditional categories of analysis. These categories are connected across, rather than along, the traditional lines between the physical sciences. Further, NLS relies on some qualitatively distinct methods that have the potential to make significant contributions to the next generation of engineering analysis. The greatest potential for NLS is the creation of new technologies by introducing fundamentally different capabilities and by integrating ideas across the normal disciplinary lines. In this regard, the recent nonlinear revolution has been compared to the early twentieth century quantum revolution. Quantum mechanics did not change the classical world. It did not reduce friction or make engines run more efficiently. Instead, it provided qualitatively new tools for use in the microscopic world. Similarly, nonlinear science will not change the linear world or undo the successes of linear approaches. However, it will provide the essential techniques for understanding, manipulating, and controlling complex systems, processes occurring far from equilibrium, and other important phenomena that underlie the naval technologies of the future. The central thesis of this report is that the nurturing of a coordinated experimental, computational, and theoretical effort in nonlinear science at the Naval Research Laboratory (NRL) is crucial to emerging Navy technologies. The elements of nonlinear science permeate naval needs from antisubmarine warfare to targeting for strategic defense. In the remainder of the report, this thesis is developed and supported in some detail. Chapter 2 provides relevant administrative and scientific background information on nonlinear science. Chapter 3 provides several detailed examples of successful transitions from basic concepts of nonlinear science to important technological applications. In Chapter 4, the heart of this report, six broad areas are examined in which Navy needs, NRL capabilities, and nonlinear science opportunities coincide. In each of these six general areas, specific problems are identified whose solutions will provide critical and in some cases rapid progress on significant naval needs. Recommendations are discussed in Chapter 5. It is argued that the continued support of a core NLS group is necessary to maintain the excellent research effort in nonlinear science and to provide technical support for, and stimulate interactions among, the many science and engineering efforts at NRL in which NLS is essential for genuine progress.