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Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a homogeneous, isotropic, linearly elastic sphere. The modes under consideration correspond to overall changes in volume and to relative uniaxial elongation or contraction. Both situations of an elastic sphere embedded under no-slip conditions in a linearly elastic, homogeneous, isotropic, infinitely extended background medium and of a free-standing elastic sphere are considered. For example, our analytical expressions are important as a basis for computational material optimization in the context of spherical soft actuators., Comment: 29 pages, 0 figures

We report high-resolution dilatometry studies on single crystals of the Shastry-Sutherland-lattice magnet NdB$_4$ supported by specific heat and magnetometry data. Our dilatometric studies evidence pronounced anomalies at the phase boundaries which imply strong magneto-elastic coupling. The evolution of the three zero-field phase transitions separating distinct antiferromagnetic phases at $TN=17.2$~K, $TIT=6.8$~K and $TLT=4.8$~K can thus be traced in applied magnetic fields which provides the magnetic phase diagrams for $B\parallel c$ up to 15~T and for $B\parallel [110]$ up to 35~T. New in-field phases are discovered for both field directions and already known phases are confirmed. In particular, phase boundaries between different phases are unambiguously shown by sign changes of observed anomalies and corresponding changes in uniaxial pressure effects. For $B||c$, we find a 1/4-magnetization plateau in addition to a previously reported plateau at 1/5 of the saturation magnetization. TN increases for $B\parallel c$ in fields up to 15~T implying that magnetic moments of the all-in/all-out structure in the high temperature AFM ordered phase are driven towards the $c$ axis in high magnetic fields. Uniaxial pressure dependencies ${\partial}T_{\mathrm{crit}}/{\partial}p_{\mathrm{c}}$ of the phase transition temperatures for magnetic fields and pressure applied along the $c$ axis are derived from the data.

Amongst the various fascinating types of material behavior featured by magnetic gels and elastomers are magnetostrictive effects. That is, deformations in shape or changes in volume are induced from outside by external magnetic fields. Application of the materials as soft actuators is therefore conceivable. Mostly, straight contraction or extension of the materials along a certain direction is discussed and investigated in this context. Here, we demonstrate that various further, different, higher modes of deformation can be excited. To this end, different spatial arrangements of the magnetizable particles enclosed by the soft elastic matrix, which constitute the materials, need to be controlled and realized. We address various different types of spatial configurations of the particles and evaluate resulting types of deformation using theoretical tools developed for this purpose. Examples are sheet-like arrangements of particles, circular or star-shaped arrangements of chain-like aggregates, or actual three-dimensional star-like particle configurations. We hope to stimulate with our work the development of experimental design and engineering methods so that selected spatial particle arrangements in magnetic gels and elastomers can be put to reality. Overall, we in this way wish to promote the transfer of these promising class of materials to real-world applications., Comment: 17 pages, 19 figures

Privacy-utility tradeoff remains as one of the fundamental issues of differentially private machine learning. This paper introduces a geometrically inspired kernel-based approach to mitigate the accuracy-loss issue in classification. In this approach, a representation of the affine hull of given data points is learned in Reproducing Kernel Hilbert Spaces (RKHS). This leads to a novel distance measure that hides privacy-sensitive information about individual data points and improves the privacy-utility tradeoff via significantly reducing the risk of membership inference attacks. The effectiveness of the approach is demonstrated through experiments on MNIST dataset, Freiburg groceries dataset, and a real biomedical dataset. It is verified that the approach remains computationally practical. The application of the approach to federated learning is considered and it is observed that the accuracy-loss due to data being distributed is either marginal or not significantly high.

Macroscopic elastic core-shell systems can be generated as toy models to be deformed and haptically studied by hand. On the mesoscale, colloidal core-shell particles and microgels are fabricated and investigated by different types of microscopy. We analyse, using linear elasticity theory, the response of spherical core-shell systems under the influence of a line density of force that is oriented radially and acts along the equator of the outer surface. Interestingly, deformational coupling of the shell to the core can determine the resulting overall appearance in response to the forces. We address various combinations of radii, stiffness, and Poisson ratio of core and shell and illustrate the resulting deformations. Macroscopically, the situation could be realized by wrapping a cord around the equator of a macroscopic model system and pulling it tight. On the mesoscale, colloidal microgel particles symmetrically confined to the interface between two immiscible fluids are pulled radially outward by surface tension., Comment: 18 pages, 5 figures, article

This study leverages the data representation capability of fuzzy based membership-mappings for practical secure distributed deep learning using fully homomorphic encryption. The impracticality issue of secure machine (deep) learning with fully homomorphic encrypted data, arising from large computational overhead, is addressed via applying fuzzy attributes. Fuzzy attributes are induced by globally convergent and robust variational membership-mappings based local deep models. Fuzzy attributes combine the local deep models in a robust and flexible manner such that the global model can be evaluated homomorphically in an efficient manner using a boolean circuit composed of bootstrapped binary gates. The proposed method, while preserving privacy in a distributed learning scenario, remains accurate, practical, and scalable. The method is evaluated through numerous experiments including demonstrations through MNIST dataset and Freiburg Groceries Dataset. Further, a biomedical application related to mental stress detection on individuals is considered.