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Register a new userElectromagnetic-Power-based Modal Classification, Modal Expansion, and Modal Decomposition for Perfect Electric Conductors
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Renzun Lian
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Traditionally, all working modes of a perfect electric conductor are classified into capacitive modes, resonant modes, and inductive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the capacitive modes are further classified into intrinsically capacitive modes and non-intrinsically capacitive modes; the resonant modes are alternatively classified into intrinsically resonant modes and non-intrinsically resonant modes, and the intrinsically resonant modes are further classified into non-radiative intrinsically resonant modes and radiative intrinsically resonant modes; the inductive modes are further classified into intrinsically inductive modes and non-intrinsically inductive modes. Based on the modal expansion corresponding to these new modal classifications, an alternative modal decomposition method is proposed. In addition, it is also proved that: all intrinsically resonant modes and all non-radiative intrinsically resonant modes constitute linear spaces respectively, but other kinds of resonant modes cannot constitute linear spaces; by including the mode 0 into the intrinsically capacitive mode set and the intrinsically inductive mode set, these two modal sets become linear spaces respectively, but other kinds of capacitive modes and inductive modes cannot constitute linear spaces.
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In computational physics and mathematical physics, modal analysis method has been one of important study topics. The central purposes of this Post-Doctoral Concluding Report are (1) to reveal the core position of energy viewpoint in the realm of electromagnetic modal analysis; (2) to show how to do energy-viewpoint-based modal analysis for various electromagnetic structures. The major conclusions of this report are that: energy conservation law governs the energy utilization processes of various electromagnetic structures, and its energy source term sustains the steady energy utilization processes; the whole modal space of an electromagnetic structure is spanned by a series of energy-decoupled modes (DMs), which dont have net energy exchange in any integral period; the DMs can be effectively constructed by orthogonalizing energy source operator, which is just the operator form of the energy source term. Specifically speaking: in classical electromagnetism, energy conservation law has five different manifestation forms, that are power transport theorem (PTT), partial-structure-oriented work-energy theorem (PS-WET), entire-structure-oriented work-energy theorem (ES-WET), Poyntings theorem (PtT), and Lorentzs reciprocity theorem (LRT) forms; the energy source terms in the first four forms are formulated as input power operator (IPO), partial-structure-oriented driving power operator (PS-DPO), entire-structure-oriented driving power operator (ES-DPO), and Poyntings flux operator (PtFO); the DMs of wave-port-fed, lumped-port-driven, externally-incident-field-driven, and energy-dissipating/self-oscillating electromagnetic structures can be constructed by orthogonalizing IPO, PS-DPO, ES-DPO, and PtFO; LRT guarantees that the obtained DMs satisfy some useful Em-Hn orthogonality relations, where the Em and Hn represent the electric field of the m-th DM and the magnetic field of the n-th DM.
Recent advances in using retrieval components over external knowledge sources have shown impressive results for a variety of downstream tasks in natural language processing. Here, we explore the use of unstructured external knowledge sources of images and their corresponding captions for improving visual question answering (VQA). First, we train a novel alignment model for embedding images and captions in the same space, which achieves substantial improvement in performance on image-caption retrieval w.r.t. similar methods. Second, we show that retrieval-augmented multi-modal transformers using the trained alignment model improve results on VQA over strong baselines. We further conduct extensive experiments to establish the promise of this approach, and examine novel applications for inference time such as hot-swapping indices.
In this paper we study the problem of learning from multiple modal data for purpose of document classification. In this problem, each document is composed two different modals of data, i.e., an image and a text. Cross-modal factor analysis (CFA) has been proposed to project the two different modals of data to a shared data space, so that the classification of a image or a text can be performed directly in this space. A disadvantage of CFA is that it has ignored the supervision information. In this paper, we improve CFA by incorporating the supervision information to represent and classify both image and text modals of documents. We project both image and text data to a shared data space by factor analysis, and then train a class label predictor in the shared space to use the class label information. The factor analysis parameter and the predictor parameter are learned jointly by solving one single objective function. With this objective function, we minimize the distance between the projections of image and text of the same document, and the classification error of the projection measured by hinge loss function. The objective function is optimized by an alternate optimization strategy in an iterative algorithm. Experiments in two different multiple modal document data sets show the advantage of the proposed algorithm over other CFA methods.
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and scientific applications, often require a large number of linear modes to obtain a small representation error. This difficulty, even for the most simple transports, originates from the inappropriateness of the decomposition structure in time dependent amplitudes of purely spatial modes. In this article an approach is discussed, which decomposes a flow field into several fields of co-moving frames, where each one can be approximated by a few modes. The method of decomposition is formulated as an optimization problem. Different singular-value-based objective functions are discussed and connected to former formulations. A boundary treatment is provided. The decomposition is applied to generic cases and to a technically relevant flow configuration of combustion physics.
Learning multi-modal representations is an essential step towards real-world robotic applications, and various multi-modal fusion models have been developed for this purpose. However, we observe that existing models, whose objectives are mostly based on joint training, often suffer from learning inferior representations of each modality. We name this problem Modality Failure, and hypothesize that the imbalance of modalities and the implicit bias of common objectives in fusion method prevent encoders of each modality from sufficient feature learning. To this end, we propose a new multi-modal learning method, Uni-Modal Teacher, which combines the fusion objective and uni-modal distillation to tackle the modality failure problem. We show that our method not only drastically improves the representation of each modality, but also improves the overall multi-modal task performance. Our method can be effectively generalized to most multi-modal fusion approaches. We achieve more than 3% improvement on the VGGSound audio-visual classification task, as well as improving performance on the NYU depth V2 RGB-D image segmentation task.
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