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In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…
Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
Periodically-driven flows are known to generate non-zero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such…
Applying machine learning to real-world medical data, e.g. from hospital archives, has the potential to revolutionize disease detection in brain images. However, detecting pathology in such heterogeneous cohorts is a difficult challenge.…
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…
Diffusion model, the state-of-the-art generative machine learning architecture, has shown promising results airfoil inverse designs. In this study, we implemented and trained a series of diffusion models on three different airfoil geometry…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
Solid-state ionic conduction is a key enabler of electrochemical energy storage and conversion. The mechanistic connections between material processing, defect chemistry, transport dynamics, and practical performance are of considerable…
In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…
Electrical conduction among cardiac tissue is commonly modeled with partial differential equations, i.e., reaction-diffusion equation, where the reaction term describes cellular stimulation and diffusion term describes electrical…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
Recent advances in diffusion models have opened new avenues for research into embodied AI agents and robotics. Despite significant achievements in complex robotic locomotion and skills, mobile manipulation-a capability that requires the…
Discriminative classifiers have become a foundational tool in deep learning for medical imaging, excelling at learning separable features of complex data distributions. However, these models often need careful design, augmentation, and…
Temporal volume images with 3D+t (4D) information are often used in medical imaging to statistically analyze temporal dynamics or capture disease progression. Although deep-learning-based generative models for natural images have been…
Transport and diffusion of heat in one dimensional (1D) nonlinear systems which {\it conserve momentum} is typically thought to proceed anomalously. Notable exceptions, however, exist of which the rotator model is a prominent case.…
Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as…
Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…