| Summary: | The illustrative description of the field-induced peculiarities of the director reorientation in the microsized nematic volumes under the effect of crossed magnetic <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">B</mi> </semantics> </math> </inline-formula> and electric <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">E</mi> </semantics> </math> </inline-formula> fields have been proposed. The most interesting feature of such configuration is that the nematic phase becomes unstable after applying the strong <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">E</mi> </semantics> </math> </inline-formula>. The theoretical analysis of the reorientational dynamics of the director field provides an evidence for the appearance of the spatially periodic patterns in response to applied large <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">E</mi> </semantics> </math> </inline-formula> directed at an angle <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">B</mi> </semantics> </math> </inline-formula>. The feature of this approach is that the periodic distortions arise spontaneously from a homogeneously aligned nematic sample that ultimately induces a faster response than in the uniform mode. The nonuniform rotational modes involve additional internal elastic distortions of the conservative nematic system and, as a result, these deformations decrease of the viscous contribution <inline-formula> <math display="inline"> <semantics> <msub> <mi>U</mi> <mi>vis</mi> </msub> </semantics> </math> </inline-formula> to the total energy <i>U</i> of the nematic phase. In turn, that decreasing of <inline-formula> <math display="inline"> <semantics> <msub> <mi>U</mi> <mi>vis</mi> </msub> </semantics> </math> </inline-formula> leads to decrease of the effective rotational viscosity coefficient <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>γ</mi> <mi>eff</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>. That is, a lower value of <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>γ</mi> <mi>eff</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, which is less than one in the bulk nematic phase, gives the less relaxation time <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>τ</mi> <mi>on</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>∼</mo> <msub> <mi>γ</mi> <mi>eff</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, when <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> is bigger than the threshold value <inline-formula> <math display="inline"> <semantics> <msub> <mi>α</mi> <mi>th</mi> </msub> </semantics> </math> </inline-formula>. The results obtained by Deuterium NMR spectroscopy confirm theoretically obtained dependencies of <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>τ</mi> <mi>on</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> on <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>.
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