Problems that admit solitons and are completely integrable have been analyzed in detail since their discovery by Zabusky and Kruskal 25 years ago. Their study has influenced the development of both mathematics and phy...
Problems that admit solitons and are completely integrable have been analyzed in detail since their discovery by Zabusky and Kruskal 25 years ago. Their study has influenced the development of both mathematics and physics during that time. The questions addressed here are: (i) Has this subject run its natural course? (ii) Will it significantly influence the nonlinear science that develops over the next decade? Supporting examples will be chosen from several disciplines, but especially from the study of water waves.
We analyze the problem of stationary self-propagating fronts in potential flow. The issues of local existence and uniqueness for solutions of the ODE describing stationary fronts, multiplicity of solutions and lineari...
We analyze the problem of stationary self-propagating fronts in potential flow. The issues of local existence and uniqueness for solutions of the ODE describing stationary fronts, multiplicity of solutions and linearized stability of a stationary front as a solution of the (hyperbolic) evolution equation are addressed. The results are illustrated in the case of the dual-source system, which is a simple model of a combustion system in which local extinction may arise. Model extensions for combustion applications are presented.
A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the ...
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A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations.
If you breadk your leg on a mountain but have a cell phone or othertransmitter with you, you would hope a rescuer could determine the direction in which to travel toreach you. Similarly, if a navy detects a transmissi...
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If you breadk your leg on a mountain but have a cell phone or othertransmitter with you, you would hope a rescuer could determine the direction in which to travel toreach you. Similarly, if a navy detects a transmission from a submarine, it would want to determinethe signal's direction of arrival (DOAto locate that sub. The problem is complicated if more thanone signal appears―especially if the number of signals is unknown―and even more complicated if youor the submarine is moving. Surprisingly, we will see that your rescuer can solve an eigenvalueproblem (involving the product of some unknown matricesand use that information to find you. TheDOA-finding algorithm we'll use is called Esprit. To understand the process, we also will useseveral matrix decompositions and illustrate the necessity of using update techniques for real-timecomputations.
The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecu...
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Two-phase heterogeneous materials arise in a plethora of natural and synthetic situations, such as alloys, composites, geological media, complex fluids, and biological media, exhibit a wide-variety of microstructures,...
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Plant-based essential oils are complex natural products composed of volatile compounds with wide applications in food, cosmetics, and pharmaceuticals. Their bioactive properties, including antimicrobial, antioxidant, ...
Plant-based essential oils are complex natural products composed of volatile compounds with wide applications in food, cosmetics, and pharmaceuticals. Their bioactive properties, including antimicrobial, antioxidant, and anti-inflammatory effects, make them promising candidates for food flavoring, preservation, and therapeutic uses. Variations in chemical composition are influenced by geographical, climatic, and extraction factors, necessitating further investigation into their functional roles. This review aims to explore the versatile applications of plant-based essential oils, emphasizing their use in food flavoring, culinary practices, and health benefits. The paper highlights their potential as natural preservatives, flavor enhancers, and bioactive agents, while also addressing challenges such as toxicity, allergenicity, and interactions with food components. A comprehensive literature review was conducted to analyze studies on the extraction methods, chemical compositions, and biological activities of essential oils. Data was gathered to evaluate their antimicrobial, antioxidant, and preservative properties, along with their impact on food quality and safety. Essential oils exhibit significant antimicrobial and antioxidant activities, enabling their use as natural preservatives in food systems, active packaging, and edible coatings. Their incorporation into products such as cheese, ice cream, and beverages has demonstrated enhanced sensory attributes and prolonged shelf life. Encapsulation techniques have shown promise in minimizing interactions with food matrices, ensuring stability, and preserving bioactivity. Plant-based essential oils represent versatile natural additives with functional and sensory benefits. Their antimicrobial, antioxidant, and flavor-enhancing properties support their use in food preservation and flavoring. Encapsulation techniques effectively address challenges related to solubility and stability, enhancing their practical applications
We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for sma...
We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small epsilon the heteroclinic connection breaks up and that the splitting between its components scales with epsilon like epsilon(gamma) exp(-beta/epsilon). We estimate beta using the singularities of the epsilon --> 0+ heteroclinic orbit in the complex plane. We then estimate gamma using linearization about orbits in the complex plane. While these estimates are not proven, they are well supported by our numerical calculations. The work described here is a special case of the theory derived by Amick et al. which applies to q-dimensional volume preserving mappings.
We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equ...
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We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The me...
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A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate values of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a sufficient number of locations are available for assimilation.
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