M.Ing. / Experimental tests have indicated that limit cycles are likely to occur in hydraulic drive systems, where backlash in the actuator seals is the dominant nonlinearity'. This study primarily deals with the analysis and synthesis of existing hydraulic drive systems to eliminate limit cycles and with establishing a design tool for the design of hydraulic drives with the object of avoiding limit cycles. Most analytical results were verified experimentally. The most general methods for the design of practical nonlinear systems are discussed. It is concluded that some form of synthesis and analysis is necessary, and that the need exists for general methods to evaluate the stability of nonlinear systems and design tools for nonlinear system design. Ageneral procedure of system analysis is given. Amathematical model of the system needs to be obtained, which can be done with the aid of bond graphs. Simulations of complex systems are recommended to verify system performance only. The first procedure of system analysis that should be followed is to systematically identify elements of the system which are not related to the cause of the limit cycle. Experimental testing is a good first step in identifying the non-critical elements. Signal flow diagrams enable the engineer quickly to determine all feedback loops of a complicated system which might be critical. Block diagrams are necessary for the application of nonlinear analysis and synthesis techniques. Hydraulic resonance, where the actuator seal acts as an oscillating mechanism, is identified as a possible cause of the limit cycle. An unusual application of the describing function, where the describing function is applied to optimize the hydraulic supply, is discussed. The transfer function of flow in a hydraulic pipe is given. With the use of the describing function, the gain margin can be studied versus different parameters of the plant. This gives insight into slightly damped conditions of the hydraulic supply that might be the cause of a limit cycle in the system. A control gain does not change the dynamic behaviour of the hydraulic supply, but only amplifies certain natural modes of the system. The design application of the describing function to nonlinear hydraulic drives is discussed. Procedures to eliminate an existing limit cycle and to design a nonlinear hydraulic drive system are proposed. Most important of all, is to design the system so that the natural frequencies of the mechanical structure and the hydraulic supply do not have any common multiples.

<p> This dissertation presents studies on several statistical-mechanical problems, many of which involve exotic many-particle systems. In Chapter 2, we present an algorithm to generate Random Sequential Addition (RSA) packings of hard hyperspheres at the infinite-time saturation limit, and investigate this limit with unprecedented precision. In Chapter 3, we study the problem of devising smooth, short-ranged isotropic pair potentials such that their ground state is an unusual targeted crystalline structure. We present a new algorithm to do so, and demonstrate its capability by targeting several singular structures that were not known to be achievable as ground states with isotropic interactions. </p><p> A substantial portion of this dissertation examines exotic many-particle systems with so-called &ldquo;collective-coordinate&rdquo; interactions. They include &ldquo;stealthy&rdquo; potentials, which are isotropic pair potentials with disordered and infinitely degenerate ground states as well as &ldquo;perfect-glass&rdquo; interactions, which have up to four-body contributions, and possess disordered and <i>unique</i> ground states, up to trivial symmetry operations. Chapters 4-7 study the classical ground states of &ldquo;stealthy&rdquo; potentials. We establish a numerical means to sample these infinitely-degenerate ground states in Chapter 4 and study exotic &ldquo;stacked-slider&rdquo; phases that arise at suitable low densities in Chapter 5. In Chapters 6 and 7, we investigate several geometrical and physical properties of stealthy systems. Chapter 8 studies lattice-gas systems with the same stealthy potentials. Chapter 9 is concerned with the introduction and study of the perfect-glass paradigm. Chapter 10 demonstrates that perfect-glass interactions indeed possess disordered and unique classical ground states&mdash;a highly counterintuitive proposition. </p><p> In Chapter 11, we use statistical-mechanical methods to characterize the spatial distribution of the prime numbers. We show that the primes are much more ordered than anyone previously thought via the structure factor. Indeed, they are characterized by infinitely many Bragg peaks in any non-zero interval of wave vectors, yet unlike quasicrystals, the ratio between the heights or locations of any two Bragg peaks is always rational. We analytically explain the locations and heights of all such peaks.</p><p>

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